If you are dealt 4 cards from a shuffled deck of 52? cards, find the probability that all 4 cards are diamondsdiamonds.

= 11/4165

Step-by-step explanation:

We are dealt 4 cards, so we will assume no replacement.

The first card:

There are 52 cards and 13 of them are diamonds

P (1st card is a diamond) = 13/52 = 1/4

The second card:

We have 1 card that is a diamond

There are 51 cards and 12 of them are diamonds

P (2nd card is a diamond) = 12/51

The third card:

We have 2 cards that are diamonds

There are 50 cards and 11 of them are diamonds

P (3rd card is a diamond) = 11/50

The fourth card:

We have 3 cards that are diamonds

There are 49 cards and 10 of them are diamonds

P (4th card is a diamond) = 10/49

P (all 4 cards are diamonds) = P (1st card is a diamond) * P (2nd card is a diamond) * P (3rd card is a diamond) * P (4th card is a diamond)

= 1/4 * 12/51 * 11/50 * 10/49

= 11/4165