Question

A card from a well shuffled deck of 52 playing cards is lost. From the  remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.

Answer 1

E₁: Lost card is king

E₂: Lost card is not king

Let A: a card drawn from remaining pack is king

`P(E_1) = 4/52 , P(E_2) = 48/52`

`P(A/E_1) = 3/51`

`P (A/E_2) = 4/51`

`P(E_1/A) = (4/52xx3/51)/(4/52xx3/51 + 48/52 xx4/51)`

`P(E_1/A) = (4xx3)/(4xx3+48xx4)`

`P(E_1/A) = 12/204`