32% of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball.
What is your question?
To find the probability that at least one of the six randomly selected women considers herself a fan of professional baseball, we can use the concept of complementary events.
First, let's find the probability that none of the six women consider themselves fans of professional baseball. The probability that a woman does not consider herself a fan is 1 - 0.32 = 0.68.
Since we have six independent events, we multiply the probabilities together:
P(none of the six women are fans) = (0.68) * (0.68) * (0.68) * (0.68) * (0.68) * (0.68) ≈ 0.09
Now, the probability of at least one woman considering herself a fan is equal to 1 minus the probability that none of them are fans:
P(at least one woman is a fan) = 1 - P(none of the six women are fans) ≈ 1 - 0.09 ≈ 0.91
Therefore, the probability that at least one of the six randomly selected women considers herself a fan of professional baseball is approximately 0.91, or 91%.