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

Question

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 (A) (1/20) (B) (3/25) (C) (12/25) (D) (3/5)

Tardigrade Admin · Accepted Answer

P ( overline m )=(20/100)=(1/5) P ( overline p )=(25/100)=(1/4) P ( overline m ∩ overline p )=(20/100)=(1/5) Required probability = P (( overline p / overline m ))=( P ( overline p ∩ overline m )/ P ( overline m ))=(3 / 25/1 / 5)=(3/5)

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

$\frac{1}{20}$

$\frac{3}{25}$

$\frac{12}{25}$

$\frac{3}{5}$

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

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

201​

253​

2512​

53​