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.

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:

Pr(the two faulty DVDs are from watchflix) =

= 0.0042

Pr(the two faulty DVDs are from Bluechest) = = 0.0022

Pr(1 is from Bluechest, 1 is from Watchflix) = = 0.01051

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

Pr( Exactly 2 are faulty) = 0.0169 = 0.017

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

step-by-step explanation:

(3rd option) - c