Question

A game at a carnival has 83 rubber ducks floating in water. The ducks are numbered 01 to 83, with the numbers written on their undersides so they can't be seen. To play, you select a duck and see what number it has. If the number is less than 60, you win a consolation prize. If the number is at least 60 but less than or equal to 70, you win a stuffed duck. If the number is greater than 70 you win a giant, stuffed banana.

Required:
a. What is the probability you win a stuffed duck?
b. What is the probability you don't win a duck or a banana?

Answer 1

a) 12.2% probability that you win a stuffed duck

b) 70.73% probability that you don't win a duck or a banana

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

`P(X \leq x) = (x - a)/(b-a)`

The probability of finding a value of X between c and d is given by the following formula:

`P(c \leq X \leq d) = (d - c)/(b-a)`

The ducks are numbered 01 to 83

Each number is equally as likely to be sorted, so
`a = 1, b = 83`

a. What is the probability you win a stuffed duck?

If the number is at least 60 but less than or equal to 70, you win a stuffed duck. So between 60 and 70.

`P(60 \leq X \leq 70) = (70 - 60)/(83 - 1) = 0.1220`

12.2% probability that you win a stuffed duck

b. What is the probability you don't win a duck or a banana?

That is, probability you win a consolation prize.

If the number is less than 60, you win a consolation prize.

That is, 59 or lower.

`P(X \leq 59) = (59 - 1)/(83 - 1) = 0.7073`

70.73% probability that you don't win a duck or a banana