Question

Jamie and Kyle ask a Magic 8-ball three questions. A Magic 8-ball has 20 possible responses for a question.

What is the probability that at least one response is ``Ask again later''?

Answer 1

There are total 20 possible responses for any question and the question is asked 3 times, there for total number of possible outcomes = 20 * 20 * 20 = 20^3
Out of these 20 responses 1 of the responses is 'Ask again later'. So there are 19 other responses.
For any response, Probablity of 'Ask again later' is 1/20.
Therefore Probablity of 'Ask again later' not coming up in 1 response is 19/20

Probablity of 'Ask again later' coming up atleat once can be computed as = 1 - Probablity of 'Ask again later' not coming up in any of the 3 responses.
= 1 - (19/20)^3 = 0.1426 Answer