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a deck of cards contains 20 cards: 14 red cards and 6 black cards. 5 cards are drawn randomly without replacement. what is the probability that more than 4 red cards are drawn?

Sagot :

reinhard10158

Step-by-step explanation:

5 cards are drawn.

"more than 4" means then exactly 5.

a probability is always

desired cases / total possible cases

we have 14 red cards and 6 black cards. in total 20 cards.

how many patterns of 5 cards are possible in total ?

that are 20 over 5 combinations :

20! / (5! × (20-5)!) = 20×19×18×17×16/(5×4×3×2) =

= 4×19×6×17×4/2 = 2×19×6×17×4 =

= 15,504 total cases

the desired cases of more than 4 red cards (= 5 red cards) is 6 over 5 combinations (how many ways to pull 5 cards out of 6 red cards) :

6! / (5! × (6-5)!) = 6

so, the probability for that is

6 / 15,504 = 1/2,584 = 0.0003869969...

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