A lot of 10 components contains 3 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective. Let B be the event that the second component drawn is defective

What is P (A) ?

Find P (B)

Find P (B|A) Are A and B independent? Explain

P (A) = 3/10 = 0.3

P (B) = 2/9 = 0.22

P (B|A) = 0.3 * 0.22 = 0.066

A and B aren't independent because after selecting the first component, it's not returned to the lot, without replacing it back, that's why the number of components available for the second drawn is nine and not ten.

Step-by-step explanation:

1. Let's review the information given to us to answer the questions correctly:

Number of defective components in the lot = 3 our of 10

2. Let A be the event that the first component drawn is defective.

What is P (A) ?

P (A) = Number of defective components in the lot/Total of the components of the lot

P (A) = 3/10 = 0.3

3. Let B be the event that the second component drawn is defective.

Find P (B)

P (B) = Number of defective components in the lot/Total of the components of the lot

P (B) = 2/9 = 0.22

4. Find P (B|A) Are A and B independent?

P (B|A) = 0.3 * 0.22 = 0.066

A and B aren't independent because after selecting the first component, it's not returned to the lot, without replacing it back, that's why the number of components available for the second drawn is nine and not ten.