Respuesta :
Answer:
[tex]p = 0.405[/tex] is the probability of a ticket having popcorn coupon
6.02% probability that exactly 2 of the tickets have popcorn coupons.
Step-by-step explanation:
For each movie ticket, there are only two possible outcomes. Either it has a popcorn coupon, or it does not. The probability of a movie ticket having a popcorn coupon is independent of other movie tickets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
If you buy 12 movie tickets, we want to know the probability that exactly 2 of the tickets have popcorn coupons.
So p is the probability of a ticket having popcorn coupon.
The probability of buying a movie ticket with a popcorn coupon is 0.405
So [tex]p = 0.405[/tex]
This probability is P(X = 2) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.405)^{2}.(0.595)^{10} = 0.0602[/tex]
6.02% probability that exactly 2 of the tickets have popcorn coupons.
