Probabilities are used to determine the chances of events
The probability that exactly 14 of the tickets have popcorn coupons is 0.1604
The parameters are given as:
[tex]n = 21[/tex] -- the sample size
[tex]r = 14[/tex] -- the count of tickets
[tex]p = 0.717[/tex] --- the probability of a movie ticket having a popcorn coupon
The probability that 14 of the 21 tickets have popcorn coupon is calculated using the following binomial probability formula
[tex]P(x =r) =^nC_r p^r(1 -p)^{n-r}[/tex]
So, we have:
[tex]P(x =14) =^{21}C_{14} * (0.717)^{14} * (1 -0.717)^{21-14}[/tex]
[tex]P(x =14) =116280 * (0.717)^{14} * (1 -0.717)^7[/tex]
[tex]P(x =14) =0.16042729141[/tex]
Approximate
[tex]P(x =14) =0.1604[/tex]
Hence, the probability that exactly 14 of the tickets have popcorn coupons is 0.1604
Read more about probabilities at:
https://brainly.com/question/15246027
