Answer:
a) 0.280
b) 0.300
c) No, preference is not independent of gender. Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not completely, statistically independent. It's very close though.
Explanation:
Let the probability that the somebody surveyed is a male be P(M)
Let the probability that somebody surveyed is female be P(F)
Let the probability that somebody surveyed picked the name-brand milk be P(N)
Let the probability that somebody surveyed picked the store-brand milk be P(St)
Let the probability that somebody surveyed picked the something else be P(So)
a) Given that an American is a male, what is the probability that he prefers name-brand milk = P(N|M) = 319/1138 = 0.280
b) Given that an American is a female, what is the probability that she prefers name-brand milk = P(N|F) = 341/1138 = 0.300
c) To investigate if the preference and gender are independent or not, we need the P(N)
P(N) = probability that an average an Average American (male or female) will prefer a nam-brand milk = 660/2276 = 0.290.
Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not statistically independent. It's very close though.