Question

To celebrate the opening of a new store, when a customer gets to the register, they get to spin a prize wheel that is equally divided into 4 parts. Depending on what part the customer lands on, they win either a 10%, 20%, 30%, or 50% discount on their entire purchase.

a) What is the probability that the first customer to win a 50% discount is the 5th customer to get to the register?

Answer 1

81 / 1024

Explanation:

Given that :

Wheel is divided into 4:

Hence, probability of winning either 10%, 20%, 30% or 50% = 1/4

Probability of winning 50% discount = 1/4

Probability of not winning 50% discount :

1 - 1/4 = (4 - 1) /4 = 3/4

Hence, probability that 50% is won by 5th customer :

(3/4) * (3/4) * (3/4) * (3/4) * (1/4)

= (3/4)^4 * (1/4)

= (81 /256) *(1/4)

= 81 / 1024