First slide

Theorems of probability

Question

The probability that a student passes a physics test is $\frac{2}{3}$ and the probability that he passes both a physics test and an English test is $\frac{14}{45}$ . The probability that passes at least one test is $\frac{4}{5}$ . The probability that he passes the English test is

Very Easy

A

$\frac{4}{9}$
B

$\frac{1}{20}$
C

$\frac{4}{5}$
D

$\frac{16}{45}$

Solution

$P (A) = \frac{2}{3}, P (A \cap B) = \frac{14}{45}$
$P (A \cup B) = \frac{4}{5}$

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

$\Rightarrow \frac{4}{5} = \frac{2}{3} + P (B) - \frac{14}{45}$

$∴ P (B) = \frac{4}{9}$

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