Question

100 students appeared for two examination. 60 passed the first, 50 passed

the second and 30 passed both. Find the probability that a student

selected at random has passed at least one examination.

Answer 1

Let S be the sample space associated with the experiment of students

who appeared for two examination. Then, n(S) = 100 Let A be the event

that students passed in first examination

$\therefore P\left(A\right)=\frac{60}{100}$

[60 students were passed in first examination]

$\therefore P\left(B\right)=\frac{50}{100}$

[50 students were passed in second examination]

$P(A\cap B)=\frac{30}{100}$

[$\because$ 30 students passed in both examination]

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

$=\frac{60}{100}+\frac{50}{100}-\frac{20}{100}=\frac{8}{100}=\frac{4}{5}$