Question

A student appears in an entrance test for two subjects—History and Sociology. The probability that the student passes History test is 2/3 and the probability that he passes both History and Sociology test is 14/45. The probability that he passes at least one test is 4/5. What is the probability that he passes the Sociology test?​

Answer 1

Answer:

I don't know this but I have tried

Answer 2

Answer:

$\frac{4}{5} = \frac{2}{3} + x - \frac{41}{45}$

$x = \frac{4}{5} + \frac{14}{45} - \frac{2}{3}$

$x = \frac{(4 \times 9) + 14 - (2 \times 15)}{45}$

$x = \frac{36 + 14 - 30}{45}$

$x = \frac{6 + 14}{45}$

$x = \frac{20}{45}$

$x = \frac{4}{9}$