Question

Suppose that out of 20% of all packages from Amazon are delivered by UPS, 12% 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? b. What is the probability that a package is not delivered by UPS if it weighs 2 lbs or more?

Answer 1

a)

X -package is delivered

Y - weight is 2 lbs or more

P(X) = 0.20

P(Y|X) = 0.12

P( Y' |X') = 0.08

P( X|Y) = P(X and Y) /P(Y)

P(X and Y) = P(Y|X) P(X) = 0.12* 0.20 = 0.024

P(Y) = P(Y|X) P(X) + P(Y|X') P(X')

= 0.12*0.20 + 0.8 * 0.92

= 0.76

hence

required probability = 0.024/0.76

= 0.0315789

b)

P(X'|Y) = P(X'and Y) /P(Y)

=    1- 0.0315789

= 0.968421