Question

Using a standard deck of cards, deal a five-card hand. What is the probability your hand contains five clubs?

Answer 1

`(49519)/(10000000)`

Step-by-step explanation:

A standard deck has 52 cards, 13 of which are clubs. The probability of dealing a single club is
`(13)/(52)`. Now, there are 12 clubs in 51 cards. The probability of a club from this deck is
`(12)/(51)`. We now continue this pattern with all other cards. All five values are:
`(13)/(52), (12)/(51), (11)/(50), (10)/(49), (9)/(48)`. Now, because these are independent probabilities and we need to find the total chance, we multiply them. Multiplying gives us
`4.9519E^(-4)` or
`0.00049519` Converting this to a fraction gives us
`(49519)/(10000000)` as our final answer.