Question

Noah randomly selects one of his eight different pairs of shoes to wear each day. Of his eight pairs of​ shoes, Noah has two pairs of boots and one pair of loafers. For how many days of the next 264 is it expected that Noah will wear either boots or​ loafers?

Answer 1

Answer:

The expected number of times that Noah wears either boots or loafers is 99.

Step-by-step explanation:

Given:-

- Noah has 8 different pairs of shoes to wear, Out of 8 pairs:

                    two pairs of boots

                    one pair of loafers

Find:-

For how many days of the next 264 is it expected that Noah will wear either boots or​ loafers?

Solution:-

- Denote an Event (A) that Noah selects a pair of boots.

- Denote an Event (B) that Noah selects a pair of loafers.

- The probability of each event is to be determined:

                p ( A ) = Pair of boots / Total pair of shoes

                p ( A ) = 2 / 8

                p ( A ) = 1/4

                p ( B ) = Pair of loafers / Total pair of shoes

                p ( B ) = 1 / 8

- The probability that Noah selects a pair of boot or loafers is independent from each other:

               p ( A U B ) = P (A) + P (B)

               p ( A U B ) = 0.25 + 0.125

                                 = 0.375

- The expected number of days out n = 264 days do we expect Noah to wear either boots or loafers.

- The number of days (trials) n = 264 days

- The probability of success = p ( A U B ) = 0.375

- The expected value = n*p

                                   = 264*0.375

                                   = 99 days