Let n be the last digit of your socialsecurity number. (e.g. the last digit of m
ID: 2915782 • Letter: L
Question
Let n be the last digit of your socialsecurity number.(e.g. the last digit of my SSN is 4) I think we need to use thisnumber in the problem.
There is a group of people that knows a secret. The probabilitythat any one person leaks the secret is 0.0n
(0.04 - for my number)
a. If there are 2 people in the group , what is the likelihood thatsomeone leaks the secret? What if there are 5 people in thegroup?
b.How many people do you need in the group to guarantee thatsomeone leaks the secret with 90% probability?
Explanation / Answer
The secret is leaked if at least one person leaks it. This isthe same thing as 1 - no one leaking it. P(not leaking secret) = 1 - .04 = .96 Assuming the 2 people are independent, the probability of both notleaking the secret is .96^2. This means the probability ofthe secret being leaked is 1 - .96^2. If you have 5 people,the formula simply becomes 1 - .96^5. Assuming n = 4 still, we now want to find how many people arerequired so that the probability of leaking the secret is90%. We want to solve .9 = 1 - .96 ^ x. .96^x = 1 - .9 = .1 x = log_.96 (.1) where log_.96 indicates the log base .96 = ln(.1) / ln(.96) = 56.4 people = 57 people (round up to ensure the secret is leaked with AT LEAST90% probability)
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