Question

Rachel rents three DVDs from Watch Flicks and two DVDs from Bluechest. The probability that a DVD is faulty is 4% for Watchflix 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.

Answer 1

Answer:

Pr( Exactly 2 are faulty) = 0.017

Step-by-step explanation:

Probability that a Watchflix DVD is faulty = 4% = 0.04

Probability that a Bluechest DVD is faulty = 5% 0.05

Probability(Exactly 2 DVD are faulty) = Pr(the two faulty DVDs are from watchflix) + Pr(the two faulty DVDs are from Bluechest) + Pr(1 is faulty from Watchflix and the other from Bluechest)

Binomial distribution is given by:

$P(r) = nCr p^{r} q^{n-r}$

Pr(the two faulty DVDs are from watchflix) =

$3C2 (0.04)^{2} (1-0.04)^{3-2} * (1-0.05)^{2}$ = 0.0042

Pr(the two faulty DVDs are from Bluechest) = $(1-0.04)^{3} 0.05^{2}$ = 0.0022

Pr(1 is from Bluechest, 1 is from Watchflix) = $3C1 * 0.04 * (1-0.04)^{2} * 2C1 * 0.05 * (1-0.05)$ = 0.01051

Pr( Exactly 2 are faulty) = 0.001386 + 0.0022 + 0.01051

Pr( Exactly 2 are faulty) = 0.0169 = 0.017