Question

If three cards are drawn without replacement from a 52 card deck, find the probability that all three are hearts. Recall that there are 4 suits in a deck: spades(black), clubs(black), diamonds(red), and hearts (red). Each suit contains 13 cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King and Ace. The Jack. Queen and King are called face cards. Round your answers to four decimals. Write your answers in the form O.XXXX! a) 0.0129 b) 0.0156 c) 0.2500 d) 0.7500

Answer 1

Let's generalise to h

Hearts, d

Diamonds, c

Clubs and s

Spades drawn from a standard deck.

These can be drawn in (13h)(13d)(13c)(13s)

ways where (13n)=13!(13−n)!n!

is the number of ways of selecting n

cards from 13

cards.

There are (52h+d+c+s)

total ways of drawing the hand from the deck.

I leave it as an exercise for the reader to calculate the values for h=d=3

and c=s=2

, or any other combination they care to consider

Explanation: