# 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

333 views

closed

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.

+1 vote
by (31.5k points)
selected by

Given : let A , B and C be three students whose chances of solving a problem is given i.e ,

P(A) = $\frac{1}{3}$, P(B) = $\frac{1}{4}$ and P(C) = $\frac{1}{6}.$

$\Rightarrow P(\overline A)=\frac{2}{3},$ P($\overline B$) = $\frac{3}{4}$ and P($\overline C$) = $\frac{5}{6}$

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)

$\frac{31}{72}$

Therefore , The probability that excatly one of them will solve the problem is$\frac{31}{72}$