Question

Suppose you draw four cards from a standard 52-card deck without replacement. What is the probability that you draw 4 hearts? Round to the nearest thousandths.

Answer 1

There are 13 heart cards in a deck of 52 cards.

Without replacement, the probability of drawing hearts will be:

`\text{ Probability = \lparen1st draw\rparen\lparen2nd draw\rparen\lparen3rd draw\rparen\lparen4th draw\rparen}`
`\text{ Probability = \lparen}(13)/(52))((12)/(51))((11)/(50))((10)/(49))`
`\text{ = }(17,160)/(6,497,400)\text{ = }(11)/(4165)\text{ = 0.00264105642}`
`\text{ Probability }\approx\text{ 0.003}`

Therefore, the probability is around 0.003