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
