Question

Refer to the previous block of questions (Section 2.3 - Exercise 15). Let E1 be the event that the wafer comes from Lot A, and let E2 be the event that the wafer is conforming. Are E1 and E2 independent? Explain.

Answer 1

The question is referring to Exercise 15 which you have not provided with the question. I am attaching a snippet of the question as an image so that it completes the question which you have asked.

Answer:

E1 and E2 are not independent because P(E2|E1) ≠ P(E2)

Step-by-step explanation:

Two events A and B are said to be independent if:

P(A|B) = P(A)

In this case, we will verify if P(E2|E1) = P(E2)

For that, we need to calculate the probability of event E2.

P(E2) = Probability that the wafer is conforming

P(E2) = No. of wafers conforming / Total no. of wafers

        = (88 + 165 + 260) / 600

        = 513/600 = 0.855

Then, we will use the conditional probability formula:

P(E2|E1) = P(E2∩E1)/P(E1)

where,

• P(E2∩E1) refers to the number of wafers which are from lot A and are conforming. we can see from the table that there are 88 such wafers.

• P(E1) refers to the number of wafers that belong to Lot A. From the table, we can see that there are 88 + 12 = 100 wafers which belong to Lot A.

So, P(E2|E1) = 88/100 = 0.88

For the events E1 and E2 to be independent, they must satisfy the equation:

P(E2|E1) = P(E2)

From our calculation we can see that:

0.88 ≠ 0.855

P(E2|E1) ≠ P(E2)

Hence, the events E1 and E2 are not independent.