Question

A survey indicates that 41% of women in the US consider reading their favonte leisure-lime activity. You randomly select four US wamen and ask them if x reading is their favorite leisure-time activity. Find the probability that at most two of them respond yes. If you were solving this problem, then what probabilities would you need to find?

Answer 1

To find the probability that at most two of the randomly selected women respond yes to reading as their favorite leisure-time activity, we need to find the probabilities for zero, one, and two women responding yes and then add these probabilities together.

Step-by-step explanation:

To find the probability that at most two of the randomly selected women respond yes to reading as their favorite leisure-time activity, we need to find the probabilities for zero, one, and two women responding yes and then add these probabilities together. Let's calculate these probabilities step by step:

P(x=0) = (0.59)^4 = 0.0980

P(x=1) = 4C1 * (0.41)^1 * (0.59)^3 = 0.3386

P(x=2) = 4C2 * (0.41)^2 * (0.59)^2 = 0.3819

Now, we can add these probabilities to find the probability that at most two of them respond yes:

P(X ≤ 2) = P(x=0) + P(x=1) + P(x=2) = 0.0980 + 0.3386 + 0.3819 = 0.8185