First slide

Theorems of probability

Question

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, then the probability that the other is also good, is

Moderate

A

$\frac{2}{13}$
B

$\frac{5}{13}$
C

$\frac{6}{13}$
D

$\frac{1}{13}$

Solution

$L e t A b e t h e e v e n t t h a t t h e f i r s t m a n g o i s g o o d . T h e n r e q u i r e d p r o b a b i l i t y i s P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)} P r o b a b i l i t y t h a t b o t h m a n g o e s a r e g o o d i s p (A \cap B) = \frac{^{6} C_{2}}{^{10} C_{2}}$
$P r o b a b i l i t y t h a t f i r s t m a n g o i s g o o d i s P (A) = \frac{C (6, 2)}{C (10, 2)} + \frac{C (6, 1) \cdot C (4, 1)}{C (10, 2)}$
$P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)} = \frac{C (6, 2)}{C (6, 2) + C (6, 1) \cdot C (4, 1)} = \frac{15}{39} = \frac{5}{13}$

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