Question

Let E₁, E₂, E₃ be three mutually exclusive events such that P(E₁) = `(2 + 3p)/6`, P(E₂) = `(2 - p)/8` and P(E₃) = `(1 - p)/2`. If the maximum and minimum values of p are p₁ and p₂, then (p₁ + p₂) is equal to ______.

Options

• `2/3`

• `5/3`

• `5/4`

• 1

Answer 1

Let E₁, E₂, E₃ be three mutually exclusive events such that P(E₁) = `(2 + 3p)/6`, P(E₂) = `(2 - p)/8` and P(E₃) = `(1 - p)/2`. If the maximum and minimum values of p are p₁ and p₂, then (p₁ + p₂) is equal to `underlinebb(5/3)`.

Explanation:

Given

P(E₁) = `(2 + 3p)/6`, P(E₂) = `(2 - p)/8` and P(E₃) = `(1 - p)/2`

According to question,

P(E₁) + P(E₂) + P(E₃) ≤ 1

`(2 + 3P)/6 + (2 - P)/8 + (1 - P)/2 ≤ 1`

26 – 3P ≤ 24

⇒ 2 ≤ 3P

⇒ `P ≥ 2/3`

So, `2/3 ≤ P ≤ 1`

Then, P₁ = 1 and P₂ = `2/3`

P₁ + P₂ = `5/3`