One class contains 5 girls and 10 boys. Second class contains 13 boys and 12 girls. A student is randomly picked from the second class and transferred to the first class. After that, a student is randomly chosen from the first class. What is the probability that this student is a boy?

My answer: I solved it by basic conditional probability method.

Probability of choosing a boy from the second class = (13/25)

Pr of choosing a boy from the first class given a boy was transferred: (11/16)

Pr of choosing a girl from the second class = (12/25)

Pr of choosing a boy given a girl was transferred: (10/16)

I plugged in the values in the formula and got the answer as 0.5437.

The textbook shows answer to be 0.6575

Where am I wrong?


What formula did you use? It must be: $$\frac{13}{25}\cdot \frac{11}{16}+\frac{12}{25}\cdot \frac{10}{16}=0.6575.$$

  • $\begingroup$ Oh correct! That was silly of me. I put this value in the denominator whereas this is the total probability. Thank you so much. $\endgroup$ – user585380 Sep 16 '19 at 3:27
  • 2
    $\begingroup$ You are welcome. Good luck. $\endgroup$ – farruhota Sep 16 '19 at 3:28

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