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?

Here is what I did:

A = .7 = Probability that a student is male.
B = .35 = Probability that a student is blond.

P(B|A) = .35

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

That is not the answer but it seems to me that I am following Bayes's theorem correctly.

Answer 1

Here is the correct answer with the work that doesn't make sense to me. This is all that was given.

P(B|A) = 35%
P(B) = 70%
P(A) = 35%

Answer = 17.5%

So they are saying:

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

P(B|A) = 35%

P(B|A) is the probability that a chosen student is male given that the student it blond.

But that is not 35%. It seems that they switched the variables to get the right answer, but it doesn't make sense logically.

Answer 2

are you trying to understand the above working?

Answer 3

yes

Answer 4

They assigned the variables opposite of what I did. But they still got the same answer for P(B|A).

But P(B|A) does not equal P(A|B)

Answer 5

The probability that a male student is blond = 35%

But the probability that a blond student is male is not known yet. That is the answer being worked on.

Answer 6

your answer is right! you probably did not play your expression well on the calculator

Answer 7

17.5% is the answer given. But it doesn't seem to fit the formula.

Answer 8

Are you saying the answer is 70% or 17.5%?

Answer 9

17.5% is the answer.

Answer 10

It seems that you didn't read everything I posted.

Answer 11

what is your question?

Answer 12

Where did I go wrong in my work?

Answer 13

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?


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

A = Probability that a student is male. = .7
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 14

please hold on.