E.math QN Lai Lai - Singapore Forums by SGClub.com
Singapore Forums by SGClub.com
Sitemap Contact Us FAQ Singapore Forums by SGClub.com
Home Photos Member List Register Mark Forums Read  
Go Back Home > Lifestyle > School Life > Math Help » E.math QN Lai Lai

Why aren't you a member of SGClub.com yet??

» Join 130,000+ other members in chatting.
» Make lots of new friends here.
» Keep up-to-date with current events.
» Participate in Club outings.
» Download lots of Free Stuff!

Registration just takes 2mins and is absolutely free so join our community today!

I Want to Choose my Own Personal Nickname Now!


Reply
 
LinkBack Thread Tools Display Modes
Old 31st August 2012, 05:20 PM   #1 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

E.math QN Lai Lai

Please state your answer.


Three dices were thrown at the same time.
Calculate the probability that
(i) the total sum of the three numbers is 17
(ii) all the three dices show different numbers

I got 1/72 for (i) and 5/9 for (ii) . My friend proclaims I am wrong

Sponsors:
EightyOne is offline  
Add to EightyOne's Reputation Reply With Quote
Old 31st August 2012, 07:09 PM   #2 (permalink)
New SGClubber
icecreamx3 is on a distinguished road

 
icecreamx3's Avatar
 
Posts: 24
Join Date: Aug 2012
Likes: 0
Liked 0 Times in 0 Posts
Gender:

Re: E.math QN Lai Lai

your answers are correct

__________________
Visit my blog at http://iamhyeon.blogspot.sg
I'm a happy blogger
icecreamx3 is offline   Add to icecreamx3's Reputation Reply With Quote
Old 31st August 2012, 07:11 PM   #3 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

Mind justifying sir?

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 31st August 2012, 07:41 PM   #4 (permalink)
Experienced SGClubber
.Memo will become famous soon enough

 
.Memo's Avatar
 
Posts: 1,601
Join Date: Nov 2010
Likes: 10
Liked 23 Times in 22 Posts
Gender:

Re: E.math QN Lai Lai

Three dices were thrown at the same time.
Calculate the probability that
(i) the total sum of the three numbers is 17
(ii) all the three dices show different numbers

i) P(5,6,6) + P(6,5,6) + P (6,6,5)
= (1/6 x 1/6 x 1/6) x 3
= 1/72

ii) 1 - P(1,1,1) - P(2,2,2) - P(3,3,3) - P(4,4,4) - P(5,5,5) - P(6,6,6)
= 1 - [(1/6 x 1/6 x 1/6) x 6]
= 35/36

__________________
Back in action
.Memo is offline   Add to .Memo's Reputation Reply With Quote
Old 31st August 2012, 07:56 PM   #5 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by .Memo View Post
Three dices were thrown at the same time.
Calculate the probability that
(i) the total sum of the three numbers is 17
(ii) all the three dices show different numbers

i) P(5,6,6) + P(6,5,6) + P (6,6,5)
= (1/6 x 1/6 x 1/6) x 3
= 1/72

ii) 1 - P(1,1,1) - P(2,2,2) - P(3,3,3) - P(4,4,4) - P(5,5,5) - P(6,6,6)
= 1 - [(1/6 x 1/6 x 1/6) x 6]
= 35/36

Part (ii) sure correct anot

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 31st August 2012, 08:19 PM   #6 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
Part (ii) sure correct anot
For part ii), memo didn't consider the 2 numbers being the same, so this approach could not be used.

Hence, The answer should be 5/9. Which is correct.

(6/6)(5/6)(4/6)
= 20/36
= 5/9

Post up your dear friend's answer, and allow us to do the analysis.

EDIT:
Let's raise the question a bar higher.

Supposed that one of the dices are biased as the bottom of the dice is heavier than the top, the probability of getting a 6 is twice of 2,3,4,5 and the probability of getting a 1 is half of 2,3,4,5. Find the probability that the 3 dices shows all different numbers.


__________________
Currently just a wanderer...

Last edited by Tetrahedron; 31st August 2012 at 08:29 PM.
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 31st August 2012, 08:42 PM   #7 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

Noooooooo. No more higher. I hate probability

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 31st August 2012, 09:11 PM   #8 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
Noooooooo. No more higher. I hate probability
What you fail to master masters you.

__________________
Are you ready to get serious?
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 31st August 2012, 09:16 PM   #9 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

Does JC have probability?

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 31st August 2012, 09:24 PM   #10 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
Does JC have probability?
JC builds on the foundation in E and A maths, so yes, definitely.

__________________
Are you ready to get serious?
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 1st September 2012, 11:50 AM   #11 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
Does JC have probability?
Yes definitely, in Statistics.

Permutations and Combinatorics are also covered. Look it up.

__________________
Currently just a wanderer...
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 1st September 2012, 03:56 PM   #12 (permalink)
Experienced SGClubber
.Memo will become famous soon enough

 
.Memo's Avatar
 
Posts: 1,601
Join Date: Nov 2010
Likes: 10
Liked 23 Times in 22 Posts
Gender:

Re: E.math QN Lai Lai

Arr didn't consider 1,1,2/ 1,2,2 blah blah...

Your question tedious sia! need consider cases...

__________________
Back in action
.Memo is offline   Add to .Memo's Reputation Reply With Quote
Old 1st September 2012, 04:19 PM   #13 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

The best part only two marks.

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 1st September 2012, 04:31 PM   #14 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
The best part only two marks.
Pretty normal in A levels.

__________________
Currently just a wanderer...
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 1st September 2012, 04:38 PM   #15 (permalink)
★ ☆ ★ ☆ ★ ☆ ★ ☆ ★
EightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of lightEightyOne is a glorious beacon of light

 
EightyOne's Avatar
 
Posts: 4,717
Join Date: May 2012
Likes: 261
Liked 293 Times in 260 Posts
Gender:

Re: E.math QN Lai Lai

Tetra, what are your subject combinations if you mind telling me?
I thinking of taking H2 chem , H2 phy , H3 mat etc

EightyOne is offline   Add to EightyOne's Reputation Reply With Quote
Old 1st September 2012, 06:03 PM   #16 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by EightyOne View Post
Tetra, what are your subject combinations if you mind telling me?
I thinking of taking H2 chem , H2 phy , H3 mat etc
Should be the combination that you are thinking about.
H2 Physics, H2 Chemistry, H2/H3 Mathematics, H1 Economics, blablabla.

Don't set on doing H3 Math so quickly. Better see how your fare for H2 before you consider H3.


Originally Posted by .Memo View Post
Arr didn't consider 1,1,2/ 1,2,2 blah blah...

Your question tedious sia! need consider cases...
Actually I should change the question slightly.

Supposed that one of the dices are biased as the bottom of the dice is heavier than the top, the probability of getting a 6 is twice of 2,3,4,5 and the probability of getting a 1 is half of 2,3,4,5. Deduce the probability that the 3 dices shows all different numbers.

__________________
Currently just a wanderer...

Last edited by Tetrahedron; 1st September 2012 at 06:24 PM.
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 1st September 2012, 07:45 PM   #17 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: E.math QN Lai Lai

For tetra's Qn,
First note that given the biased die, for 13 ideal throws, we should get {1,2,2,3,3,4,4,5,5,6,6,6,6}.

Let P be the probability function, nPr denote permutation and nCr denote combination.
P(3 different integers)
=P(3 integers∈[2,5])+P('1' and 2 other integers∈[2,5])+P('6' and 2 other integers∈[2,5])+P('1','6' and 1 other integer∈[2,5])
=(8/13)(6/13)(4/13)+3C1(1/13)(8/13)(6/13)+3C1(4/13)(8/13)(6/13)+3P3(1/13)(4/13)(8/13)
=1104/2197

If you don't know the P's and C's, 3C1=3 basically refers to the fact that
P('1' and 2 other integers∈[2,5])=P(1,x,y)+P(x,1,y)+P(x,y,1) and
P('6' and 2 other integers∈[2,5])=P(6,x,y)+P(x,6,y)+P(x,y,6),
and these 2 probabilities have 3 terms hence 3C1=3.

And then 3P3=6 refers to the fact that
P('1','6' and 1 other integer∈[2,5])=P(1,6,x)+P(1,x,6)+(x,1,6)+P(6,1,x)+P(6,x,1)+P(x, 6,1)
which have 6 terms hence 3P3=6.

I hope I am correct.

__________________
Are you ready to get serious?
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 1st September 2012, 08:13 PM   #18 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: E.math QN Lai Lai

Let's raise this another bar higher xD

I have an unbiased 6-sided die. I throw the die twice and multiply the 2 numbers together to get another number. Say I do this 5 times and obtain 5 numbers. Find the probability that the sum of these 5 numbers is divisible by 4.

__________________
Are you ready to get serious?
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Old 1st September 2012, 08:39 PM   #19 (permalink)
Honesty is a virtue~
Tetrahedron is a jewel in the roughTetrahedron is a jewel in the rough

 
Tetrahedron's Avatar
 
Posts: 1,519
Join Date: Sep 2010
Likes: 16
Liked 156 Times in 111 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by Betakuwe View Post
For tetra's Qn,
First note that given the biased die, for 13 ideal throws, we should get {1,2,2,3,3,4,4,5,5,6,6,6,6}.

Let P be the probability function, nPr denote permutation and nCr denote combination.
P(3 different integers)
=P(3 integers∈[2,5])+P('1' and 2 other integers∈[2,5])+P('6' and 2 other integers∈[2,5])+P('1','6' and 1 other integer∈[2,5])
=(8/13)(6/13)(4/13)+3C1(1/13)(8/13)(6/13)+3C1(4/13)(8/13)(6/13)+3P3(1/13)(4/13)(8/13)
=1104/2197

If you don't know the P's and C's, 3C1=3 basically refers to the fact that
P('1' and 2 other integers∈[2,5])=P(1,x,y)+P(x,1,y)+P(x,y,1) and
P('6' and 2 other integers∈[2,5])=P(6,x,y)+P(x,6,y)+P(x,y,6),
and these 2 probabilities have 3 terms hence 3C1=3.

And then 3P3=6 refers to the fact that
P('1','6' and 1 other integer∈[2,5])=P(1,6,x)+P(1,x,6)+(x,1,6)+P(6,1,x)+P(6,x,1)+P(x, 6,1)
which have 6 terms hence 3P3=6.

I hope I am correct.
Sorry, your working is too complex for secondary school level. Look at my rephrased question, and think again. .

(I cannot give answer, as it will give the answer away automatically. =X)


Originally Posted by Betakuwe View Post
Let's raise this another bar higher xD

I have an unbiased 6-sided die. I throw the die twice and multiply the 2 numbers together to get another number. Say I do this 5 times and obtain 5 numbers. Find the probability that the sum of these 5 numbers is divisible by 4.
Basket, Olympiad level question, don't scare little kids la.

__________________
Currently just a wanderer...

Last edited by Tetrahedron; 1st September 2012 at 08:48 PM.
Tetrahedron is offline   Add to Tetrahedron's Reputation Reply With Quote
Old 1st September 2012, 09:40 PM   #20 (permalink)
Addicted SGClubber
Betakuwe has a spectacular aura about

 
Betakuwe's Avatar
 
Posts: 874
Join Date: Sep 2010
Likes: 6
Liked 48 Times in 41 Posts
Gender:

Re: E.math QN Lai Lai

Originally Posted by Tetrahedron View Post
Sorry, your working is too complex for secondary school level. Look at my rephrased question, and think again. .
Are you referring to the combination and permutation? If you are then I've explained it in the latter part of the post.

What do you expect anyway, P(3 different numbers)=1-P(2 or more same numbers)? That's kinda tedious.

I believe my probability question is still very doable for 'O'/'A' level maths students

edit: some correction

OK, it's not as tedious as I thought.
P(2 or more same numbers)=P(2 '1's)+P(2 '6's)+P(2 same integers∈[2,5])
=P(3 '1's)+P(2 '1's and an integer∈[2,6])+P(3 '6's)+P(2 '6's and an integer∈[1,5])+P(3 same integers∈[2,5])+P(2 same integers∈[2,5] and another different one)
=(1/13)³+3(1/13)²(12/13)+(4/13)³+3(4/13)²(9/13)+(8/13)(2/13)²+3(8/13)(2/13)(11/13)
=1093/2197

1-1093/2197=1104/2197

idk if this is the answer you want, you are a very strict marker

__________________
Are you ready to get serious?

Last edited by Betakuwe; 1st September 2012 at 10:18 PM.
Betakuwe is offline   Add to Betakuwe's Reputation Reply With Quote
Reply

Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Two interesting math questions(O level additional math) megaman123 Math Help 6 27th August 2012 09:46 PM
Parents whose child do not like Math, this could be the solution for you!!! Math Monkey is FUN MATH! blueface7 Tuition Services & Educational Supplies 0 18th February 2010 03:12 PM
H2 math need O level A math background? shaunshen School Life 16 31st January 2010 10:11 PM
Doing The Math janice SGClub Cafe 2 11th March 2008 12:55 AM

» Sponsors
Watch Free Movies Online
Celebrity Gossip
Food Delivery

» Facebook Fans
» What's Going On?
Title, Username, & Date
Repost comment.
Stupid court of appeal gives red light running driver who hit pedestrian 15% discount
Mum's Kitchen Catering and Cherish Delights get licences suspended after nearly 40 people...
[PMD-pedestrian rules] Singapore Court judges are high handed and biased or court rep
Post anything random on this thread.
Ritter Sport chocolate recalled due to undeclared allergen
Aoki Hagane no Arpeggio: Ars Nova
I really hate my mother!!!
Transcend RDF9K2 All-in-One Card Reader
Transcend ESD250C, a portable SSD that’s super classy
How PAP exploited racial differences to impose FASCIST rule over Singapore.
Up to S$7250 of government $ misused for buying each vote in Singapore?
Funky Fields organic vegan spreadable recalled due to 'undisclosed allergen'
100 hawksbill turtles released into the sea after rare hatching on Sentosa
Inspirational Songs
MOH, SFA investigating after 18 typhoid fever cases in 3 weeks
By militarily invading Hong Kong, Xi Jingping is setting in motion, the wheels of nuc
Deng XiaoPing original vision for HKG- China reunification was for the two to unite a
HSA warns against three products
Warning : Blacklist buyer/adopter Alert
Featured Photos
by marisoljames322
· · ·
Member Galleries
20359 photos
13619 comments
by marisoljames322
· · ·
Member Galleries
20359 photos
13619 comments
by pdsubbu
· · ·
Member Galleries
20359 photos
13619 comments
by Vikas Dhar
· · ·
Photography
35 photos
36 comments
by aaudreygan
· · ·
Guy Photos
1581 photos
946 comments
by aaudreygan
· · ·
Girl Photos
4351 photos
28606 comments
by a8paris
· · ·
Guy Photos
1581 photos
946 comments
by a8paris
· · ·
Guy Photos
1581 photos
946 comments
by aaricia
· · ·
Girl Photos
4351 photos
28606 comments
by aaricia
· · ·
Girl Photos
4351 photos
28606 comments

 

All times are GMT +8. The time now is 05:20 AM.


Powered by vBulletin
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
Copyright© 2004-2013 SGClub.com. All rights reserved.