Question

A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards chosen are clubs and the third card is black if the cards are chosen with replacement, and if the cards are chosen without replacement.A) The cards are chosen with replacement. ______B) The cards are chosen without replacement. ______

Answer 1

We will have the following:

First, we have that an standard deck of cards has 52 cards in total, and 13 cards of each description (hearts, clubs, spades and diamonds) and 26 are red and 26 are black.

Now, with this information we will calulate the probabilities:

A)

*Without replacement:

`p=(13)/(52)\cdot(12)/(51)\cdot(26)/(50)\Rightarrow p=(13)/(425)\Rightarrow p=0.03058823529\ldots`

*With replacement:

`p=(13)/(52)\cdot(13)/(52)\cdot(26)/(52)\Rightarrow p=(1)/(32)\Rightarrow p=0.03125`