Two integrated circuits made from the same wafer are tested

Two integrated circuits made from the same wafer are tested. Each IC either passes the test or fails the test. The event that the first IC fails the test is called A. The event that the second IC fails the test is called B. The probability of A, P(A)=0.03. The probability of B, P(B)=0.03. The probability that both ICs fail is P(A Intersection B)is 0.015. What is the conditional probability P(B|A) the the 2^nd IC fails the test given that the first IC failed the test? Sampling with replacement The NAU student ID number is a 9-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. How many possible student ID numbers are there? What is the probability of getting the ID number that is all 1s, 111111111? How many student ID numbers have a 1 as the first digit? What is the probability of getting a student ID number with a 1 as the first digit?

Solution

1)solution

the probability of A ,P(A)=0.03

the probability of B,P(B)=0.03

the probability of both ICs failed

that is P(AB)=0.015

P(B/A)=?

P(AB)/P(A)=0.015/0.03

       P(B/A) =0.5

2)solution

information needed for this 2n problem