Question

At a certain college, 49% of the students are male and 51% are female. In addition, 20% of the men and

10% of the women are taking Japanese classes. The student is selected at random. If the selected student
attends Japanese lessons, what is the probability that the student is female?

Answer 1

0.339, or approximately 33.9%

Explanation:

We can solve this problem using Bayes' theorem. Let F denote the event that the selected student is female, and J denote the event that the selected student is taking Japanese classes. We want to find the probability of F given J, which we can write as P(F|J).

Using the law of total probability, we can decompose the probability of J as follows:

P(J) = P(J|F)P(F) + P(J|M)P(M)

where M denotes the event that the selected student is male. We can calculate the probabilities on the right-hand side of this equation as follows:

P(J|F) = 0.1 (from the problem statement)

P(F) = 0.51 (from the problem statement)

P(J|M) = 0.2 (from the problem statement)

P(M) = 0.49 (from the problem statement)

Plugging in these values, we get:

P(J) = 0.10.51 + 0.20.49 = 0.149

Now we can use Bayes' theorem to find P(F|J):

P(F|J) = P(J|F)P(F) / P(J)

Plugging in the values we calculated earlier, we get:

P(F|J) = 0.1*0.51 / 0.149 = 0.339

Therefore, the probability that the selected student is female given that they attend Japanese classes is 0.339, or approximately 33.9%.

Hope this helps!