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 49th cereal box, what is the probability of getting the toy you want in any given cereal box?

Answer 1

The probability of getting the toy you want in any given cereal box is of 0.0204 = 2.04%.

Explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected number of trials for r sucesses is:

`E = (r)/(p)`

If, on average, you get the toy you want in every 49th cereal box, what is the probability of getting the toy you want in any given cereal box?

This means that
`E = 49, r = 1`

So

`49 = (1)/(p)`

`49p = 1`

`p = (1)/(49)`

`p = 0.0204`

The probability of getting the toy you want in any given cereal box is of 0.0204 = 2.04%.

Answer 2

The probability of getting the toy in any given cereal box is
`(1)/(49)`.

Explanation:

Given,

On average, we get a toy in every 49th cereal box,

That is, in every 49 boxes there is a toy,

So, the total outcomes = 49,

Favourable outcomes ( getting a toy ) = 1

Since, we know that,

`\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}`

Hence, the probability of getting the toy in any given cereal box =
`(1)/(49)`