Refer to Exercise 10. Let Y be the number of chips tested up to and including the second acceptable chip.

a. What is the smallest possible value for Y?

b. What is the probability that Y takes on that value?

c. Let X represent the number of chips that are tested up to and including the first acceptable chip. Find P(Y = 3|X = 1).

d. Find P(Y = 3|X = 2).

e. Find P(Y = 3).

Answer :

Step 1 of 6 :

Given, from a large population, micro processing chips are randomly sampled one by one.

These chips are tested to determine if they are acceptable for a certain application.

From the population 90% of the chips are acceptable.

Where, P(A) = acceptable chips

= 90%

P(B) = unacceptable chips.

= 10%

Step 2 of 6 :

The claim is to find the smallest possible value of Y.

If both first two chip are acceptable, then Y = 2

Therefore, Y = 2 is the smallest possible value.

Step 3 of 6 :

b)

The claim is to find the probability that Y takes on the value.

When the first two chips are acceptable

P(Y = 2) = P(acceptable ) P(acceptable )

= (0.9) (0.9)

= 0.81

the probability that Y takes on the value is 0.81