A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing $15$ oranges out of which $12$ are good and $3$ are bad ones will be approved for sale.

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Let $A, B,$ and $C$ be the respective events that the first, second, and the third drawn orange is good.

Therefore, probability that first drawn orange is good, $\mathrm{P}(\mathrm{A})=\frac{12}{15}$

The oranges are not replaced.

Therefore, probability of getting second orange good, $\mathrm{P}(\mathrm{B})=\frac{11}{14}$

Similarly, probability of getting third orange good, $\mathrm{P}(\mathrm{C})=\frac{10}{13}$

The box is approved for sale, if all the three oranges are good.

Thus, probability of getting all the oranges good $=\frac{12}{15} \times \frac{11}{14} \times \frac{10}{13}=\frac{44}{91}$

Therefore, the probability that the box is approved for sale is $\frac{44}{91}$.

Similar Questions

One bag contains $5$ white and $4$ black balls. Another bag contains $7$ white and $9$ black balls. A ball is transferred from the first bag to the second and then a ball is drawn from second. The probability that the ball is white, is

If an integer is chosen at random from first $100$ positive integers, then the probability that the chosen number is a multiple of $4$ or $6$, is

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happens is $\frac{1}{{12}}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2},$ then

  • [IIT 1993]

An experiment has $10$ equally likely outcomes. Let $\mathrm{A}$ and $\mathrm{B}$ be two non-empty events of the experiment. If $\mathrm{A}$ consists of $4$ outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is

  • [IIT 2008]

If two events $A$ and $B$ are such that $P\,(A + B) = \frac{5}{6},$ $P\,(AB) = \frac{1}{3}\,$ and $P\,(\bar A) = \frac{1}{2},$ then the events $A$ and $B$ are