Question

What is the probability that, out of a random sample of 4 Americans, exactly 4 own a cat as a pet, given that the Gallup organization found that 28% of Americans own a cat?

Answer 1

The probability that exactly 4 out of 4 Americans own a cat as a pet, given that 28% of Americans own a cat, is approximately 0.008.

Step-by-step explanation:

To find the probability that exactly 4 out of 4 Americans own a cat as a pet, given that 28% of Americans own a cat, we can use the binomial distribution.

The formula for the probability mass function of a binomial distribution is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k successes, C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success, and n is the number of trials.

In this case, n = 4, k = 4, and p = 0.28. Plugging these values into the formula, we get:

P(X=4) = C(4, 4) * 0.28^4 * (1-0.28)^(4-4)

Since C(4, 4) = 1, the equation simplifies to:

P(X=4) = 0.28^4 * (1-0.28)^(4-4)

Calculating this, we find that the probability is approximately 0.008.