Question

Probability of solving the specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ receptively. If both try to solve the problem independently, find the probability that
(I) the problem is solved
(II) exactly one of them solves the problem

Answer 1

P(A)=1/2 P(B)=1/3

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

Since A and B are independent P(A$\cap$B)=P(A)*P(B)=1/6

i)Therefore P(AUB)=1/2+1/3-1/6=2/3

P(A)=1/2 P(B)=1/3

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

Since A and B are independent

P(A$\cap$B)=P(A)*P(B)=1/6

Therefore P(AUB)=1/2+1/3-1/6=2/3

ii)Exactly one of them solved P(A or B)=P(A)+P(B)-2P(A$\cap$B)=1/2