Question

A question in CBS 211 is given to two students A and B. The probabilities in favour of A solving the question are 6 to 9 and against B solving the question are 10 to 12. If both A and B attempt solving the question, find the probability of the question being solved

Answer 1

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

We have that

$$P(A)=\frac{6}{6+9}=\frac{2}{5}, P(B)=\frac{12}{10+12}=\frac{6}{11}$$

Since the events A and B are independent, then

$$P(A\cap B)=P(A)P(B)$$

Hence

$$P(A\cup B)=P(A)+P(B)-P(A)P(B)$$

$$P(A\cup B)=\frac{2}{5}+\frac{6}{11}-\frac{2}{5}\cdot\frac{6}{11}=\frac{8}{11}$$