A shipment of 5000 printed circuit boards contains 46 that a

A shipment of 5000 printed circuit boards contains 46 that are defective. Two boards will be chosen at random, without replacement. Consider the two events E₁ = event that the first board selected is defective and E₂ = event that the second board selected is defective.

(a) Are E₁ and E₂ dependent events?

A. Yes

B. No    

(b) Let not E₁ be the event that the first board selected is not defective (the event E₁^c). What is P(not E₁)?

(c) How do the two probabilities P(E₂ | E₁) and P(E₂ | not E₁) compare?

A. 2 * P(E₂ | E₁) = P(E₂ | not E₁)

B. P(E₂ | E₁) = 2 * P(E₂ | not E₁)    

(d) Based on your answer to Part (c), would it be reasonable to view E₁ and E₂ as approximately independent?

A. Yes

B. No   

Solution

P(E1) = P( Board is defective) = 46 / 5000 = 0.092
P(E2) = P ( Second is also defecctive) = 45 / 4999 = 0.009001

a)
Yes, they are, the outcome of choosing the first card has affected the outcome of choosing the second card, making these events dependent

b)
P(not E1) = 1 - P(E1) = 1 - 46/500 = 227/250 = 0.908