Question

If `E_1 and E_2` are two events associated with a random experiment such that `P (E_2)=0.35, P (E_1 or E_22)=0.85 and P(E_1 and E_2)=0.15,` then `P(E_1)` is (A) `.25` (B) `.35` (C) `.65` (D) `.75`

Answer 1

Let `P(E_(1)) = x`. Then,
`P(E_(1) or E_(2)) = P(E_(1)) + P(E_(2)) - P(E_(1) and E_(2))`
`rArr 0.85 = x + 0.35 - 0.15`
`rArr x = (0.85 - 0.35 + 0.15) = 0.65`
Hence, `P(E_(1)) = 0.65.`