Question

If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/3` and P(B) = `(1 - x)/4`, then the set of possible values of x lies in the interval ______.

Options

• [0, 1]

• `[1/3, 2/3]`

• `[-1/3, 5/9]`

• `[-7/9, 4/9]`

Answer 1

If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/3` and P(B) = `(1 - x)/4`, then the set of possible values of x lies in the interval `underlinebb([-1/3, 5/9]`.

Explanation:

Since events A and B are mutually exclusive

∴ P(A) + P(B) = 1

⇒ `(3x + 1)/3 + (1 - x)/4` = 1

⇒ 12x + 4 + 3 – 3x = 12

⇒ 9x = 5

⇒ x = `5/9`

∴ `x ∈[-1/3, 5/9]`