Question

54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not. You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10 trials).

Answer 1

Answer: the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets is 0.23

Step-by-step explanation:

We would assume a binomial distribution for the number of tickets sold to a movie with and without popcorn coupon. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 54.4% = 54.4/100 = 0.544

q = 1 - p = 1 - 0.544

q = 0.456

n = 10

x = r = 6

Therefore,

P(x = 6) = 10C6 × 0.544^6 × 0.456^(10 - 6)

P(x = 6) = 210 × 0.0259 × 0.043

P(x = 6) = 0.23