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
