If 1 + 3 p 3 , 1 − p 4 and 1 − 2 p 2 are probabilities of mutually exclusive events of a random experiment, then the range of p is

Step-by-step solution

Since, the probability lies between 0 and 1 . 0 ≤ 1 + 3 p 3 ≤ 1 , 0 ≤ 1 − p 4 ≤ 1 , 0 ≤ 1 − 2 p 2 ≤ 1 ⇒ 0 ≤ 1 + 3 p ≤ 3 , 0 ≤ 1 − p ≤ 4 , 0 ≤ 1 − 2 p ≤ 2 ⇒ − 1 3 ≤ p ≤ 2 3 , − 3 ≤ p ≤ 1 , − 1 2 ≤ p ≤ 1 2 … i Again, the events are mutually exclusive 0 ≤ 1 + 3 p 3 + 1 - p 4 + 1 - 2p 2 ≤ 1 ⇒ 0 ≤ 1 3 - 3 p ≤ 1 2 ⇒ 1 3 ≤ p ≤ 1 3 3 … ii From Eqs. (i) and (ii), we get max - 1 3 , - 3 - 1 2 1 3 ≤ p ≤ min 2 3 1 1 2 1 3 3 ⇒ 1 3 ≤ p ≤ 1 2