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

Big guy up there done wrote a whole pg. The answer is 99 days. Have a good day.

Answer 2

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

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