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  • 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 1/10

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}

B.\frac{2}{5}

C.\frac{9}{20}

D.\frac{1}{3}
 

Answers (1)

Let A be the event that students failed in physics.

As per the question, 30% students failed in physics.
∴ P(A) = 0.30
Similarly, if we denote the event of failing in maths with B.
We get P(B) = 0.25

And probability of failing in both subjects can be represented using intersection as
P (A ∩ B) = 0.1
To find- a conditional probability of failing of student in physics given that she has failed in mathematics.
The situation can be represented mathematically as-
P(A|B) =?

Using the fundamental idea of conditional probability, we know that:
\mathrm{P}(\mathrm{E} \mid \mathrm{F})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{F})}$ where $\mathrm{E}$ \& F denotes 2 random events.
$$ \therefore P(A \mid B)=\frac{P(A \cap B)}{P(B)} $$
\Rightarrow P(A \mid B)=\frac{0.1}{0.25}=\frac{10}{25}=\frac{2}{5}$
Our answers clearly match with option B
\therefore$ Option $(\mathrm{B})$  is the only correct choice.

Posted by

infoexpert22

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