Question

In your​ area, 31​% of firms are owned by women. You call local

firms at random in order to sell them accounting software. You
phone 6 local businesses at random.
​What is the probability that 2 of the 7 are owned by women?

Answer 1

To calculate the probability that exactly 2 out of 7 firms are owned by women, use the binomial probability formula with n=7, k=2, and p=0.31. The probability is approximately 0.03162, or 3.162%.

Step-by-step explanation:

To calculate the probability that exactly 2 out of 7 firms are owned by women, we need to 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 binomial coefficient.

In this case, n = 7, k = 2, and p = 0.31 (the probability that a firm is owned by a woman). The binomial coefficient C(7, 2) can be calculated as C(7, 2) = 7! / (2!(7-2)!), which is equal to 21. Plugging in these values into the formula, we get:

P(x=2) = 21 * (0.31)^2 * (1-0.31)^(7-2)

= 21 * 0.31^2 * 0.69^5

= 0.03162

So, the probability that exactly 2 out of 7 firms are owned by women is approximately 0.03162, or 3.162%.