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  4. In a college, 20 % students fail in mathematics, 25 % in physics, and 12 % in both subjects. A student of this college is selected at random. The probability that this student who has failed in mathematics would have failed in physics too, is

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Q. In a college, $20 \%$ students fail in mathematics, $25 \%$ in physics, and $12 \%$ in both subjects. A student of this college is selected at random. The probability that this student who has failed in mathematics would have failed in physics too, is

Probability - Part 2

Solution:

$P (\overline{ m })=\frac{20}{100}=\frac{1}{5}$
$P (\overline{ p })=\frac{25}{100}=\frac{1}{4} $
$P (\overline{ m } \cap \overline{ p })=\frac{20}{100}=\frac{1}{5}$
Required probability $= P \left(\frac{\overline{ p }}{\overline{ m }}\right)=\frac{ P (\overline{ p } \cap \overline{ m })}{ P (\overline{ m })}=\frac{3 / 25}{1 / 5}=\frac{3}{5}$