Question

A college class is 70% male. 35% of the total number of students are blond, and 35% of the male students are blond.

If a blond student is chosen at random, what is the probability that the student is male?

Answer 1

Here is my work. Please tell me where I am going wrong. I will include the formulas that I use.

P(A) = Probability that a student is male. = .7
P(B) = Probability that a student is blond. = .35
P(B|A) = .35

Now to find P(A|B) which is the probability that a blond student is male, I will use Bayes's theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(A|B) = (.35 * .7) / .35

P(A|B) = .7

The probability that a blond student is male is 70%. But this answer is wrong. Where did I go wrong?

Answer 2

IMHO your method and answer are correct. Perhaps your source of the 'correct answer' has it wrong?

Answer 3

I suppose that must be it.

Answer 4

For further confirmation, I also did a probability tree and once again got the same result as you did :)