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Old 7th March 2012, 11:18 PM   #1 (permalink)
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Probability

Two circles shown have radii x and 3x. (refer to attachment)

a) A point is chosen, at random, inside the larger circle. Find, in the simplest fractional form, the probability that this point is in the shaded area.

b) Find, in its simplest form, the ratio circumference of the large circle: sum of circumferences of the two circles

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Old 7th March 2012, 11:47 PM   #2 (permalink)
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Re: Probability

The two questions are very basic questions that test the basics of probability, I have a feeling that you might don't understand probability at all.

Okay, I'll show you the working then maybe put some explanation.
a)Area of shaded region
= area of big circle - area of small circle
= (pi)(3x)^2 - (pi)(x)^2
= (pi)(9x^2) - (pi)(x^2)
= (8x^2)(pi)

Probability of a point in the shaded region
= (area of shaded region)/(area of the whole big circle)
= [(8x^2)(pi)] / [(9x^2)(pi)]
= 8/9 = 0.88888... % (if they want it in decimals)

Basically when you have a question like this, that ask you what is the probability(chances) of a random point chosen in a certain area that is part of a large space, you take the area of the small region and divide it by the whole area.

b) You know circumference is the perimeter of a circle right? ok so,
Circumference of the big circle = 2*3x*(pi) = 6x(pi)
Circumference of big circle+small circle = 6x(pi) + 2*x*(pi) = 6x(pi) + 2x(pi) = 8x(pi)

So ratio of
circumference of big circle : circumference of both circle = 6x(pi) : 8x(pi) = 3 : 4

I have feeling that I'm doing your homework for you and you are just gonna copy this crap. Whether you already know how to do it but you're too lazy too calculate or you really did not know how to do, hopefully you can tell that these questions are really basic after reading through, so you should expect exams and tests to be harder.

edit: oops i put in the wrong values, thanks knyghtryder for correction


Last edited by Betakuwe; 8th March 2012 at 12:00 AM.
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Old 7th March 2012, 11:50 PM   #3 (permalink)
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Re: Probability

8/9 obvious.

3/4. betakuwe is wrong


Last edited by knyghtryder; 7th March 2012 at 11:55 PM.
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Old 8th March 2012, 12:00 AM   #4 (permalink)
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Re: Probability

Originally Posted by knyghtryder View Post
8/9 obvious.

3/4. betakuwe is wrong
Fixed, thanks for note.

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