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 ____________.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{3}{4}$
A, B, C → independent events
Using dot and cross method to get
$P(A∪B∪C)=P(A)+P(B)+P(C)−P(A∩B)−P(A∩C)−P(B∩C)+P(A∩B∩C)$
$=P(A)+P(B)+P(C)-P(A)P(B)-P(B)P(C)-P(C)P(A)-P(A)P(B)P(C)$
$=\frac{3}{4}$