Question

In your​ area, ​23% of firms are owned by women. You call local firms at random in order to sell them accounting software. You phone 5 local businesses at random. What is the probability that 2 of the 5 are owned by​ women?

Option 1: 0.266
Option 2: 0.329
Option 3: 0.126
Option 4: 0.720

Answer 1

To find the probability that 2 out of the 5 businesses are owned by women, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that 2 out of the 5 businesses are owned by women, we can use the binomial probability formula. The formula is:

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

Where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the combination of n trials taken k at a time. In this case, n = 5, k = 2, and p = 0.23.

Plugging the values into the formula, we get:

P(X=2) = C(5, 2) * 0.23^2 * (1-0.23)^(5-2) = 10 * 0.23^2 * 0.77^3 = 0.329

Therefore, the probability that 2 out of the 5 businesses are owned by women is 0.329.