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?

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