Question

Two cards are drawn without replacement from an ordinary deck. Find the probability that two clubs are drawn. The probability is (Simplify your answer. Type an integer or a simplified fraction.)

Answer 1

A standard deck of cards contains 52 cards, of which 26 are red and 26 are black, 13 are of each suit (diamonds, hearts, clubs, spades) and of which 4 are of each domination

(Ace, 1,2,3,4,5,6,7,8,9,10,jack,queen and king).

In this we have 13 of the 52 cards are clubs;

$Probability = \frac{favourable outcomes}{Total outcomes}$

The probabilty is the number of favourable outcomes to the total possible outcomes.

The probabilty of selecting club card on the first draw;

$P(clubs) = \frac{13}{52} = \frac{1}{4}$

After one club card is selected, now we are left with 12 cards of clubs and 51 cards in total (without replacement -> not putting back the drawn card)

Now probabilty of selecting again clubs;

$P(clubs) = \frac{12}{51}= \frac{4}{17}$

So probabilty that the two clubs are drawn

$P(2 clubs)= \frac{1}{4}*\frac{4}{17} = \frac{1}{17}$
If you like the answer please give THUMBS UP. Thank you.