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

Question

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:

$\frac{1}{10}$
$\frac{2}{5}$
$\frac{9}{20}$
$\frac{1}{3}$

✓

Answer

$\frac{2}{5}$

Solution:

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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