Question

You purchase boxes of cereal until you obtain one with the collector's toy you want. If, on average, you get the toy you want in every 18th cereal box, what is the probability of getting the toy you want in any given cereal box? (Round your answer to 3 decimal places.)

Answer 1

Answer:

The probability of getting the toy you want in any given cereal box is p=0.056.

Step-by-step explanation:

On average, you get the toy you want in every 18th cereal box.

This value corresponds to the mean of a geometric distribution, where it is expected that you get 17 "failures" before the first "success".

The mean of the geometic distribution, whose value is 18, can be written as:

$E(X)=\dfrac{1}{p}=18$

where p is the probability of "success": getting the collector's toy you want.

Then, p has a value of 1/18≈0.056.