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 <u>P(E2|E1) ≠ P(E2)</u>
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Step-by-step explanation:
Two events A and B are said to be independent if:
<u>P(A|B) = P(A)</u>
In this case, we will verify if <u>P(E2|E1) = P(E2)</u>
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
<u>P(E2|E1) ≠ P(E2)</u>
Hence, the events E1 and E2 are not independent.
