Final answer:
a) The probability that 7 Americans own a cat as a pet is approximately 0.0027. b) The probability that ALL 7 Americans do not own a cat as a pet is approximately 0.9973. c) The probability that at least one of 7 Americans owns a cat as a pet is approximately 0.0027.
Step-by-step explanation:
a) To find the probability that 7 Americans own a cat as a pet, we use the binomial probability formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where n is the number of trials, k is the number of successful trials, p is the probability of success, and (nCk) is the binomial coefficient.
Plugging in the values, we have:
P(X = 7) = (7C7) * (0.29)^7 * (1-0.29)^(7-7)
Simplifying, we get:
P(X = 7) ≈ 0.0027
b) To find the probability that ALL 7 Americans do not own a cat as a pet, we simply calculate the complement of the probability that 7 Americans own a cat as a pet:
P(X = 0) = 1 - P(X = 7) = 1 - 0.0027 ≈ 0.9973
c) To find the probability that at least one of 7 Americans owns a cat as a pet, we calculate the complement of the probability that none of them own a cat:
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.9973
≈ 0.0027