Question

Probability that 'A' speaks truth is `4/5`. A coin is taked. A reports that head appears. the probability that actually there was head is

Options

• `4/5`

• `1/2`

• `1/5`

• `2/5`

Answer 1

`4/5`

Explanation:

Let E₁ = A speaks the truth.

E₂ = A does not speak the truth.

P(E₁) = `4/5`  ......(Given)

∴ P(E₂) = `1 - P(E_1) = 1 - 4/5 = 1/5`

'A' is an event that a head appears

`P(A/E_1) = 1/2`, When `A' quotes head

It is a head when 'A' does not speak the truth.

Probability of getting a head,

`P(A/E_2) = 1/2`

Probability that actually it is head = `P(E_1/A)`

∴ `P(E_1/A) = (P(E_1)P(A/E_1))/(P(E_1)P(A/E_1) + P(E_2)P(A/E_2))`

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

= `(4/5)/(4/5 + 1/5)`

= `4/5`