Answer: the probability that more than 3 of the tickets have popcorn coupons is 0.951
Explanation:
We would assume a binomial distribution for the event of buying a movie ticket with a 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 = 0.608
q = 1 - p = 1 - 0.608
q = 0.392
n = 10
P(x > 3) = 1 - P(x ≤ 3)
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
Therefore,
P(x = 0) = 10C0 × 0.608^0 × 0.392^(10 - 0) = 0.000086
P(x = 1) = 10C1 × 0.608^1 × 0.392^(10 - 1) = 0.0013
P(x = 2) = 10C2 × 0.608^2 × 0.392^(10 - 2) = 0.0093
P(x = 3) = 10C3 × 0.608^3 × 0.392^(10 - 3) = 0.038
P(x ≤ 3) = 0.000086 + 0.0013 + 0.0093 + 0.038 = 0.049
Therefore,
P(x > 3) = 1 - 0.049 = 0.951