Question

If you are dealt 5 cards at random from a standard deck of playing cards, what is the probability that at most 4 of them are spades?

Answer 1

Explanation:

No of ways in which 5 cards are chosen is
`N=^(52)C_5`

No of ways in which at most 4 cards are spades
`N_0=`Total ways-5 spades

`=^(52)C_5-^(13)C_5`

Probability that at most 4 cards are spade
`P=(N_0)/(N)`

`P=(^(52)C_5-^(13)C_5)/(^(52)C_5)`

`P=(2598960-1287)/(2598960)`

`P=(2597673)/(2598960)=0.9995`