Question

A bag contain $10$ mangoes out of which $4$ are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is

• A. $\frac{1}{3}$
• B. $\frac{8}{15}$
• C. $\frac{5}{18}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{5}{18}$

Number of ways of selecting $2$ good mangoes ${=}^6{C}_2=15$
The number of ways that at least one of the two selected mangoes is to be good
${=}^6{C}_1{\times }^9{C}_1=6\times 9=54$
Required probability $=\frac{15}{54}=\frac{5}{18}$