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Old 7th December 2011, 07:25 PM   #1 (permalink)
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Simple Probability -Help

This coastal region has a mean crime rate of 12 crimes per year. The authorities monitor the region closely and record crime occurrences once every 3 months and rate the safety of the region (for that span of 3 months) according to the number of crimes that occur, as follows:

"Mildly Risky" if at most 1 crime occurs, "risky" if more than 1 but at most 3 crimes occur and "very risky" if more than 3 crimes occur.

The coastal region will be closed to the public if in a given year, the region receives 3 or more "very risky" ratings. Find the probability that at the end of a given year, the region will be closed to public.

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Old 7th December 2011, 09:42 PM   #2 (permalink)
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Re: Simple Probability -Help

Here are the detailed solutions, hope it helps. Peace.


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Old 7th December 2011, 09:48 PM   #3 (permalink)
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Re: Simple Probability -Help

Thanks whitecorp ! I was told to use a multinomial approach by evaluating the "risky" and "mild risky" .

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Old 7th December 2011, 09:53 PM   #4 (permalink)
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Re: Simple Probability -Help

No problem. You don't have to evaluate the "risky " and "mildly-risky" probabilities separately but can simply group them together, since we know the sum of probabilities for these two categories are complementary to the probability for the "very risky" rating,

This is an instance of a Poisson distribution embedded within a Binomial distribution.

Peace.


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Old 7th December 2011, 10:06 PM   #5 (permalink)
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Re: Simple Probability -Help

A true-false question is to be posed to a husband and wife team on a quiz show. Both the husband and the wife will, independently, give the correct answer with probability p = 0.6. The couple decided to use the following strategy to give their answers. Both of them consider the question independently and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to be given.

Find the conditional probability that the couple give the correct answer given that they disagree.

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Old 7th December 2011, 10:43 PM   #6 (permalink)
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Re: Simple Probability -Help

Method 1:
Since the couple already disagreed, then the outcome of whether a correct answer is given simply rests on the tossing of a coin.

Required conditional probability =0.5 (shown)

Method 2:

P(the couple disagree)= P(husband gives correct answer)* P (wife gives wrong answer)+
P(wife gives correct answer)* P (husband gives wrong answer)
= (0.6)*(0.4)+(0.6)*(0.4)=0.48

P( the couple disagree but give the correct answer) = (0.48)* (0.5)=0.24

Hence, required conditional probability = 0.24/0.48 =0.5 (shown)

Hope this helps. Peace.

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