Notice that this is compounded probability, since first, we know that the selected person is a woman, and then we need to find the probability of being a woman selecting Target for shopping.
So our first original set is the total of shoppers interviewed (so we need to add the number of men and women shopers for that)
Men = 15 + 105 + 37 + 20+ 53 + 7 + 13 = 250
Total women: 261
Grand total: 261 + 250 = 511
Therefore the probability of beaing a woman the person selected at random is:
261/511
the probability of being a woman to be a preferred Target shopper is:
67/261
Therefore , the conditional probability will give us:
P(A/B) = P(A and B)/P(B)
P(target shopper given that the shopper is a woman) = P(target shopper and woman) / P(woman)
That means we need the quotient:
P (target shopper and woman) = 67/261
P woman+ 261/511
the quotient gets converted the product of the following fractions:
67/261 * 511/261 = 0.50259
which is the decimal form of the percent: 50.259% and which rounded to the nearest hundredth of a percent gives:
50.26%