Practicing Success
A problem in mathematics is given to three students whose chances of solving it are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ respectively, the probability that the problem is solved is ____________. |
$\frac{1}{4}$ $\frac{3}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ |
$\frac{3}{4}$ |
The correct answer is Option (2) → $\frac{3}{4}$ A, B, C → independent events Using dot and cross method to get $P(A∪B∪C)=P(A)+P(B)+P(C)−P(A∩B)−P(A∩C)−P(B∩C)+P(A∩B∩C)$ $=P(A)+P(B)+P(C)-P(A)P(B)-P(B)P(C)-P(C)P(A)-P(A)P(B)P(C)$ $=\frac{3}{4}$ |