Question

Probability that A speaks truth is `4/5` . A coin is tossed. A reports that a head appears. The probability that actually there was head is ______.

Options

• `4/5`

• `1/2`

• `1/5`

• `2/5`

Answer 1

Probability that A speaks truth is `4/5`. A coin is tossed. A reports that a head appears. The probability that actually there was head is `underline(4/5)`.

Explanation:

Let E₁ = the coin will show the head

E₂ = The coin will show the head

P(E₁) = P(E₂) = `1/2`

E = A says heads are revealed

P(heads come up and A tells the truth)

= `P(E/E_1)`

= `4/5`

P(Tips come out and A is not telling the truth)

= `P(E/E_2)` 

= `1/5`

Intended process = `(4/5 xx 1/2)/((4/5 xx 1/2) + (1/5 xx 1/2))`

= `4/4 + 1`

= `4/5`