Given the probability that A can solve a problem is 2/3, and the probability that B can solve the same problem is %, find the probability that
(i)at least one of A and B will solve the problem
(ii)none of the two will solve the problem
Given : Here probability of A and B that can solve the same problem is given , i.e., P(A) = 
and P(B) = 
P(
) = 
and P(
) = 
Also, A and B are independent . not A and not B are independent.
To Find: i) atleast one of A and B will solve the problem
Now , P(atleast one of them will solve the problem) = 1 – P(both are unable to solve)
= 1 - P(
)
= 1- P(
) 
P(
)
= 1- 
= 
Therefore , atleast one of A and B will solve the problem is 
ii) none of the two will solve the problem
Now, P(none of the two will solve the problem) = P(
)
= P(
) 
P(
)
= 
= 
Therefore , none of the two will solve the problem is 