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