You draw two cards from a standard deck without replacement. What is the probability of drawing two hearts?
回答 (3)
2016-08-02 7:27 pm
In a standard deck, there are 52 cards including 13 hearts.
The number of ways of drawing 2 cards from a deck of 52 cards
= C(52, 2)
= 52! / (50! 2!)
= 1326
The number of ways of drawing 2 cards from the 13 hearts
= C(13, 2)
= 13! / (11! 2!)
= 78
P(drawing 2 hearts from a deck)
= 78/1326
= 1/17
The number of ways of drawing 2 cards from a deck of 52 cards
= C(52, 2)
= 52! / (50! 2!)
= 1326
The number of ways of drawing 2 cards from the 13 hearts
= C(13, 2)
= 13! / (11! 2!)
= 78
P(drawing 2 hearts from a deck)
= 78/1326
= 1/17
2016-08-02 7:24 pm
There are 13 hearts in a deck of 52 cards.
So the probability of the first card being a heart is (13/52) or (1/4).
After the first heart is drawn, there are 12 hearts left out of 51 cards. So the probability of another heart is (12/51)
Probability of both happening is the product of the individual probabilities:
(1/4)(12/51)
(1/1)(3/51)
1/17 or 0.0588
So the probability of the first card being a heart is (13/52) or (1/4).
After the first heart is drawn, there are 12 hearts left out of 51 cards. So the probability of another heart is (12/51)
Probability of both happening is the product of the individual probabilities:
(1/4)(12/51)
(1/1)(3/51)
1/17 or 0.0588
2016-08-02 7:25 pm
1 in 16
收錄日期: 2021-04-21 19:28:44
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