Choose the correct answer from the given four options. In a colle… - Vidyadip

MCQ

Choose the correct answer from the given four options. In a college, $30\%$ students fail in physics, $25\%$ fail in mathematics and $10\% $ fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is :

A
$\frac{1}{10}$
✓
$\frac{2}{5}$
C
$\frac{9}{20}$
D
$\frac{1}{3}$

✓

Answer

Correct option: B.

$\frac{2}{5}$

Here, $\text{P}_{(\text{Ph})}=\frac{30}{100}=\frac{3}{10}$
$\text{P}_{(\text{M})}=\frac{25}{100}=\frac{1}{4}$
And $\text{P}_{(\text{M}\cap\text{Ph})}=\frac{10}{100}=\frac{1}{10}$
$\therefore\text{P}\Big(\frac{\text{Ph}}{\text{M}}\Big)=\frac{\text{P}(\text{Ph}\cap\text{M})}{\text{P}(\text{M})}$
$=\frac{\frac{1}{10}}{\frac{1}{4}}=\frac{2}{5}$

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