23- Diane Bruns is the mayor of a big city. Lately, he has been worrying about t

Question

23- Diane Bruns is the mayor of a big city. Lately, he has been worrying about the Possibility that large numbers of people who collect unemployment insurance actually have A job in secret. Its assistants estimate that 40% of the unemployment insurance beneficiaries enter In this category, but Mrs Bruns is not convinced. He asks one of his assistants to make a Investigation of 10 insurance beneficiaries taken at random.

A) If the assistants of the mayor are right, what is the probability that the individuals investigated Have a job ?

B) If the mayor's assistants are correct, what is the probability that only three of the Investigated individuals have work?

Explanation / Answer

a) Since 40% of unemployment insurance beneficiaries have a job;
and 10 people are randomly investigated, the probably that all 10 of them have a job is = (0.4)10 = 0.001048576;

b) For only 3 of them to have a job, the probability is:
10 C 3 (0.4)3 (1-0.4)10-3 = 10*9*8/3*2 * (0.4)3 (0.6)7= 0.214990848

(10C3 is taken because any 3 people from the 10 can have a job so 10C3 triplets can be formed out of 10 people)

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