Question

The Gallup organization found that 27% of Americans own a cat as a pet. Find the probability five Americans own a cat as a pet. Round your answer to four decimal places.

Answer 1

The probability that five randomly selected Americans all own a cat, given that 27% of Americans own a cat, is approximately 0.0010 when rounded to four decimal places.

Step-by-step explanation:

The student is asking about calculating the probability that five randomly selected Americans all own a cat as a pet, given that 27% of Americans own a cat. Since each selection is independent of the others, this is a binomial probability problem.

To find the probability that all five own a cat, we raise the probability of a single person owning a cat to the fifth power:

Probability = (0.27)5

Calculating this gives the probability that all five own a cat:

Probability ≈ 0.275 ≈ 0.0010 (to four decimal places)

Answer 2

The probability of five Americans owning a cat as a pet is approximately 0.0014, or about 0.14%.

Assuming that owning a cat is an independent event for each American, the probability of five Americans owning a cat can be calculated using the binomial probability formula. Here's how:

p: Probability of one American owning a cat = 27% = 0.27

n: Number of Americans = 5

Apply the binomial probability formula:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

where:

k is the number of successes (Americans owning a cat) in this case, k = 5

(n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials. It can be calculated as n! / (k! * (n-k)!)

P(5 Americans owning a cat) = (5 choose 5) * 0.27^5 * (1-0.27)^(5-5)

= 1 * 0.27^5 * 0.73^0

≈ 0.001364

Rounding to four decimal places, the probability is approximately 0.0014.