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Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P(exactly one of A, B occurs) = `5/9`, is ______.

#### Options

`1/4`

`2/9`

`1/3`

`5/12`

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#### Solution

Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P(exactly one of A, B occurs) = `5/9`, is `underlinebb(5/12)`.

**Explanation:**

Probability(Exactly one of A and B) = `5/9`

⇒ P(A) + P(B) – 2P(A)P(B) = `5/9`

⇒ p + 2p – 4p^{2} = `5/9`

⇒ 36p^{2} – 27p + 5 = 0

⇒ (12p – 5)(3p – 1) = 0

⇒ p = `1/3` or `5/12`

∴ p_{max} = `5/12`

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