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.
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.
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
An event has odds in favour $4 : 5$, then the probability that event occurs, is
An event has odds in favour $4 : 5$, then the probability that event occurs, is
Let $A$,$B$ and $C$ be three events such that $P\left( {A \cap \bar B \cap \bar C} \right) = 0.6$, $P\left( A \right) = 0.8$ and $P\left( {\bar A \cap B \cap C} \right) = 0.1$, then the value of $P$(atleast two among $A$,$B$ and $C$ ) equals
Let $A$,$B$ and $C$ be three events such that $P\left( {A \cap \bar B \cap \bar C} \right) = 0.6$, $P\left( A \right) = 0.8$ and $P\left( {\bar A \cap B \cap C} \right) = 0.1$, then the value of $P$(atleast two among $A$,$B$ and $C$ ) equals
Fill in the blanks in following table :
$P(A)$
$P(B)$
$P(A \cap B)$
$P (A \cup B)$
$0.35$
...........
$0.25$
$0.6$
Fill in the blanks in following table :
| $P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
| $0.35$ | ........... | $0.25$ | $0.6$ |
A die is tossed thrice. Find the probability of getting an odd number at least once.
A die is tossed thrice. Find the probability of getting an odd number at least once.
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that First ball is black and second is red.
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that First ball is black and second is red.