The probability that exactly 6 out of them are women is 0.176
According to the statement
Number of selected pet owner randomly is 9. So, Here in this case n=9.(number of randomly selected owners).
Number for which have to find the probability is 6. So, Here in this case x=6.
Find the probability by a use of BINOMIAL THEOREM
So, n!/((n-x)!*x!) = 9!/((9-6)!*6!) = 84
Now, find out the probability of success p and probability of failure (1-p)=q.
From here we get p = 0.8 and q= 0.2
Now, use p^x = (0.8)^6 = 0.2621
Then use q^(n-x) = (0.2)^(9-6) = 0.008
Now, Multiply the results obtained to get the probability is
84*0.2621*0.008 = 0.176
So, The probability that exactly 6 out of them are women is 0.176
Learn more about probability here brainly.com/question/25870256
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