The probabilities of A, B, C solving a problem are 1/3, 1/4 and 1/6, respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.
Given : let A , B and C be three students whose chances of solving a problem is given i.e , P(A) = 
, P(B) = 
and P(C) = 
.
P(
) = 
, P(
) = 
and P(
)= 
To Find: The probability that excatly one of them will solve it .
Now, P(excatly one of them will solve it) = P(A and not B and not c) +P (B and not A and not C) +P (C and not A and not B)
= P( A 
) + P(B 
) + P(C 
)
= P(A) 
P(
) 
P(
) + P(B) 
P(
) 
P(
) + P(C) 
P(
)
P(
)
= [
] + [
] + [
]
= 
+ 
+ 
= 
Therefore , The probability that excatly one of them will solve the problem is 
1