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

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4/9

16/65

1/20

4/5

answer is A.

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Detailed Solution

$\begin{array}{l} P (A) = \frac{2}{3}, P (A \cap B) = \frac{14}{45}, P (A \cup B) = \frac{4}{5} \\ P (A \cup B) = P (A) + P (B) - P (A \cap B) \\ \Rightarrow \frac{4}{5} = \frac{2}{3} + P (B) - \frac{14}{45} \\ ∴ P (B) = \frac{4}{9} \end{array}$

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