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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability2 Marks
Question
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, other wise, 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.
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Answer

Let A, B, and C be the respective events that the first, second, and third drawn oranges good.
Therefore,probability that first drawn orange is  good = P(A) = $\frac{12}{15}$.
The oranges are not replaced. Therefore,probability of getting second orange good = P(B) = $\frac{11}{14}$ .
Similarly, probability of getting third orange good = P(C) = $\frac{10}{13}$
The box is approved for sale if all the three oranges are good. 
$\therefore$ Required probability $ = \frac{{12}}{{15}} \times \frac{{11}}{{14}} \times \frac{{10}}{{13}}$$=\frac{44}{91}$
$$

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