Question

Events A, B, C are mutually exclusive events such that P(A)= 3x+1 3 ,P(B)= 1-x 4 and P(C)= 1-2x 2 . The set of all possible values of x are in the interval A. [0, 1] B. [-1/3,1/2] C. [1/3,2/3] D. [1/3,13/3] Select the correct answer from above options

Answer 1

Correct Answer - B It is given that the events A, B, C, are mutually exclusive. Therefore, P ( A ) ≥ 0 , P ( B ) ≥ 0 , P ( C ) ≥ 0 , and P ( A ∪ B ∪ C ) ≥ 0 P ⇒ P ( A ) ≥ 0 , P ( B ) ≥ 0 , P ( C ) ≥ 0 , and P ( A ) + P ( B ) + P ( C ) ≥ 0 ⇒ ⇒ 3 x + 1 3 ≥ 0 , 1 − x 4 > 0 , 1 − 2 x 2 ≥ 0 ⇒ , and, 3 x + 1 3 + 1 − x 4 + 1 − 2 x 2 ≥ 0 3 ⇒ x > − 1 3 , x ≤ 1 , x ≤ 1 2 and 1 − 3 x > 0 ⇒ ⇒ − 1 3 ≤ x ≤ 1 2 and x ≤ 1 3 ⇒ ⇒ − 1 3 ≤ x ≤ 1 2 ⇒ x ∈ [ − 1 / 3 , 1 / 2 ] ⇒