Question

Rachel rents three DVDs from Watchflicks and two DVDs from Bluechest. The probability that a DVD is faulty is 4% for Watchflicks and 5% for Bluechest. All DVD rentals being faulty or otherwise are independent of each other. Calculate the probability that exactly two DVDs rented by Rachel are faulty. a) 0.015 b) 0.017 c) 0.019 d) 0.021 e) 0.023

Answer 1

Answer:

Option b) is correct Answer

Binomial distribution: P(X) = nCx p^x q^n-x

Number of rentals from Watchflicks = 3

Number of rentals from Bluechest = 2

P(exactly two DVDs are faulty) = P(2 DVDs from Watchflicks are faulty) + P(2 DVDs from Bluechest are faulty) + P(1 DVD from Watflicks and 1 DVD from Bluechest is faulty)

= 3x0.04²x0.96 x 0.95² + 0.96³ x 0.05² + 3x0.04x0.96² x 2x0.95x0.05

= 0.017

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