Question

Suppose the probability experiment is to draw two cards, without replacement, from a well-shuffled, standard poker deck.What is the chance both cards will be a spade

Answer 1

Answer: The chance both cards will be a spade is
`(1)/(17)` .

Explanation:

We know that , in a standard deck , the total number of cards = 52

The number of spades = 13

If a person selected 2 cards,

The total number of combination of selecting 2 cards out of 52 =
`^(52)C_2`

The number of combination of selecting 2 spade cards out of 13 =
`^(13)C_2`

Then , the probability that both cards will be a spade=
`(^(13)C_2)/(^(52)C_2)`

`((13!)/(2!11!))/((52!)/(2!*50!))\ \ [\because\ ^nC_r=(n!)/(r!(n-r)!)]`

`=(13*12)/(51*52)`

`=(1)/(17)`

Hence, the chance both cards will be a spade is
`(1)/(17)` .