Question

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.

Options

• `3/4`

• `52/867`

• `39/50`

• `22/425`

Answer 1

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is `underlinebb(39/50)`.

Explanation:

Let, E₁ = Event in which spade is missing

P(E₁) = `1/4`  ...(i)

`P(bar(E_1))` = 1 – P(E₁)

`P(bar(E_1))` = `3/4`  ...(ii)

 E = Event in which drawn two cards are spade.

P(E) = `((1/4)((""^12C_2)/(""^51C_2)) + (3/4)((""^13C_2)/(""^51C_2)) - (3/4)((""^13C_2)/(""^51C_2)))/((1/4)((""^12C_2)/(""^51C_2)) + (3/4)((""^13C_2)/(""^51C_2))`

P(E) = `((1/4)((12 xx 11)/(51 xx 50)) + (3/4)((13 xx 12)/(51 xx 50)) - (3/4)((13 xx 12)/(51 xx 50)))/((1/4)((12 xx 11)/(51 xx 50)) + (3/4)((13 xx 12)/(51 xx 50))`

P(E) = `((12 xx 11) + (3)(13 xx 12) - (3)(13 xx 12))/((12 xx 11) + (3)(13 xx 12))`

P(E) = `11/50`

Required probability = 1 – P(E)

= `1 - 11/50`

= `39/50`