Kashvi, Kalyani and Sara of class 12 are given a problem in Accounts whose respective probabilities of solving are $\frac{2}{5},\frac{1}{4}$ and $\frac{1}{6}$. They were asked to solve it independently.
The probability that either only Kalyani or Kashvi or Sara solves it is:
Answer & explanation
Correct answer: option 1
Using venn diagram
P(only one of these solves the problems)
$=P(A)+P(B)+P(C)-2P(A∩B)-2P(B∩C)-2P(A∩C)+3P(A∩B∩C)$
$=\frac{2}{5}+\frac{1}{4}+\frac{1}{6}-\frac{2×2×1}{5×4}-\frac{2×1×1}{4×6}-\frac{2×2×1}{5×6}+\frac{3×2}{4×5×6}$
$=\frac{48+30+20-24-10-16-6}{120}=\frac{104-50}{120}$
$=\frac{9}{20}$