A standard deck of cards is purchased, and the deck includes 3 jokers. This means if the jokers are included, the deck contains 5 5 cards. Teresa is playing a game in which she is dealt 8 cards from a deck that includes the jokers. What is the probability that Teresa's hand includes at least one joker?

The probability is

Step-by-step explanation:

We know that Teresa is playing a game in which she is dealt 8 cards from a deck that includes 3 jokers and 52 common cards (a total of 55 cards).

Let's define the following random variable :

: '' Number of jokers in the hand of Teresa ''

We need to find

This probability is equivalent to :

is the probability of having none jokers in the 8 card hand.

In order to find we are going to count all the cases in which (given that we are in presence of an equally - likely sample space)

We calculate as :

We define the combinatorial number

In the denominator we have which represents all the ways in which we can extract 8 cards from the deck of 55 cards.

In the numerator we have the product of  (which represents all the ways in which we can choose 8 cards from the 52 common cards) and    (which represents that from the total of 3 jokers we extract 0)

 If we perform the operation we find that :

Finally,

The probability is