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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?

User Evan Moran
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1 Answer

5 votes

Answer:

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!

User Felipe Ardila
by
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