Question

If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is 

A. > . 5 

B. .5 

C. ≤ .5 

D. 0

Answer 1

Let E₁ be the event that A fails in an examination

and E₂ be the event that B fails in an examination

Then, we have

P (E₁) = 0.2 and P (E₂) = 0.3

Now, we have to find the P (either E₁ or E₂ fails)

∴ P(either E₁ or E₂ fails) = P(E₁) + P(E₂) – P(E₁⋂ E₂)

≤ P(E₁) + P(E₂)

≤ 0.2 + 0.3

≤ 0.5

Hence, the correct option is (C)