# The probability that Hemant passes in English is (2/3), and the probability that he passes in Hindi is (5/9).

Question:

The probability that Hemant passes in English is (2/3), and the probability that he passes in Hindi is (5/9). If the probability of his passing both the subjects is (2/5), find the probability that he will pass in at least one of these subjects.

Solution:

let A denot the event that Hemant passes in english and B denote the event that hemant passes in hindi .

Given : $P(A)=\frac{2}{3}, P(B)=\frac{5}{9}, P(A$ and $B)=\frac{2}{5}$

To find : Probability that he will pass in at least one of these subjects. $=\mathrm{P}(\mathrm{A}$ or $\mathrm{B})$

Formula used: $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$

$P(A$ or $B)=\frac{2}{3}+\frac{5}{9}-\frac{2}{5}$

$P(A$ or $B)=\frac{30+25-18}{45}=\frac{37}{45}$

$P(A$ or $B)=\frac{37}{45}$

The probability that he will pass in at least one of these subjects. $=P(A$ or $B)=\frac{37}{45}$