Respuesta :
Answer:
a) 12.2% probability that you win a stuffed duck
b) 70.73% probability that you don't win a duck or a banana
Step-by-step 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.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The probability of finding a value of X between c and d is given by the following formula:
[tex]P(c \leq X \leq d) = \frac{d - c}{b-a}[/tex]
The ducks are numbered 01 to 83
Each number is equally as likely to be sorted, so [tex]a = 1, b = 83[/tex]
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.
[tex]P(60 \leq X \leq 70) = \frac{70 - 60}{83 - 1} = 0.1220[/tex]
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.
[tex]P(X \leq 59) = \frac{59 - 1}{83 - 1} = 0.7073[/tex]
70.73% probability that you don't win a duck or a banana
