Question

A basket contains ten mangoes out of which 3 are rotten. If three mangoes are chosen at random, find the probability that all the mangoes will be good

• A. $\frac{3}{24}$
• B. $\frac{3}{7}$
• C. $\frac{11}{24}$
• D. $\frac{7}{24}$

Answer 1

Answer: (D)

$\frac{7}{24}$

A basket contains ten mangoes out of which 3 are rotten And if three mangoes are chosen at random

$\therefore$ Total number of possible outcomes $n\left(S\right)=$${}^{10}{C}_3$
All the three mangoes are good. ${}^{10}{C}_3$ The number of favourable outcomes $n\left(E\right)=$${}^7{C}_3$
$P$(all the three are good) $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{{}^7{C}_3}{{}^{10}{C}_3}=\frac{\left(7\right)\left(6\right)\left(5\right)}{\left(10\right)\left(9\right)\left(8\right)}=\frac{7}{24}$