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.

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Again, what is your question?

To find the probability of a certain number of women considering themselves fans of professional baseball out of the six women you randomly selected, you can use the binomial probability formula.

The binomial probability formula is:

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

Where:
- P(X = k) is the probability of getting exactly k successes (in this case, women considering themselves fans of professional baseball).
- (n choose k) is the number of ways to choose k successes from n trials.
- p is the probability of success (in this case, the proportion of women who consider themselves fans of professional baseball).
- (1 - p) is the probability of failure.

Now let's calculate the probability for each possible number of women considering themselves fans:

P(X = 0) = (6 choose 0) * (0.32^0) * ((1-0.32)^(6-0))
P(X = 1) = (6 choose 1) * (0.32^1) * ((1-0.32)^(6-1))
P(X = 2) = (6 choose 2) * (0.32^2) * ((1-0.32)^(6-2))
P(X = 3) = (6 choose 3) * (0.32^3) * ((1-0.32)^(6-3))
P(X = 4) = (6 choose 4) * (0.32^4) * ((1-0.32)^(6-4))
P(X = 5) = (6 choose 5) * (0.32^5) * ((1-0.32)^(6-5))
P(X = 6) = (6 choose 6) * (0.32^6) * ((1-0.32)^(6-6))

Calculating each of these probabilities will give you the probability for each number of women considering themselves fans.