Question

Three sisters Neha, Sneha and Keya have respective probabilities of breaking a dish in the kitchen are $\frac{1}{3},\frac{1}{2}$ and $\frac{4}{5}$. If any of them is selected by their mother to help her in the kitchen, find the probability that a dish will be broken

• A. $\frac{27}{80}$
• B. $\frac{49}{90}$
• C. $\frac{31}{64}$
• D. $\frac{31}{90}$

Answer 1

The correct option is B $\frac{49}{90}$

$Eachgirlisequalylikelytogetselectedwithprobability=1/3Probabilitythatnehaisselectedgivendishisbroken=\frac{1}{3}\ast \frac{1}{3}=\frac{1}{9}Probabilitythatsnehaisselectedgivendishisbroken=\frac{1}{3}\ast \frac{1}{2}=\frac{1}{6}Probabilitythatkeyaisselectedgivendishisbroken=\frac{1}{3}\ast \frac{4}{5}=\frac{4}{15}Probabilitythatdishisbroken=\frac{1}{9}+\frac{1}{6}+\frac{4}{15}=\frac{49}{90}$