Question

In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand containing a spade flush.

Answer 1

0.00597

Explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

`\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}`

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

`=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}`

`=(^(20)C_5)/(^(52)C_5)`

`=((20!)/(5!15!))/((52!)/(5!47!))`

`=(15504)/(2598960)`

= 0.00597