Question

In a Science quize, two teams work independently on a problem. They are allowed a maximum of 15 minutes to solve the problem The probabilities between them will solve the problem are 1/2 and 1/3 respectively. Calculate tge probability that the problem will be solved jn the 15 minutes allowed

Answer 1

Probability of solving the problem by A, $P(A)=\dfrac{1}{2}.$ Probability of solving the problem by B, $P(B)=\dfrac{1}{3}.$

Since the problem is solved independently by A and B

$$P(A\cap B)=P(A)P(B)=\dfrac{1}{2}(\dfrac{1}{3})=\dfrac{1}{6}$$

Probability that the problem will be solved jn the 15 minutes allowed

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

$$=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{6}=\dfrac{2}{3}$$