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!