Question

Suppose that 30% of all packages from Amazon are delivered by UPS. 15% of the packages that are delivered by UPS weighs 2 lbs or more. Also, 8% of the packages that are not delivered by UPS weighs less than 2 lbs. a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more

Answer 1

probability = 0.05761

Step-by-step explanation:

given data

P(X) = 30% = 0.30

P(Y | X) = 15% = 0.15

P( Y' | X') = 8% = 0.08

here X is package is delivered

and Y is weight 2 lbs or more

solution

here we can say that P(X and Y) is express as

P(X and Y) = P(Y|X) × P(X) .............1

put here value and we get

P(X and Y) = 0.15 × 0.30

P(X and Y) = 0.045

so probability of package is delivered of weighs 2 lbs or more P (Y) is

P (Y) = P(Y|X) × P(X) + P(Y|X') × P(X') ............2

put here value we get

P (Y) = 0.15 × 0.30 + 0.8 × 0.92

P (Y) = 0.781

so required probability is =
`(P(X\ and\ Y) )/(P(Y))`

probability =
`(0.045)/(0.781)`

probability = 0.05761