Question

Twenty draws are made with replacement from a standard deck of playing cards. Find the chance of

(1) getting all non-aces

(2)not getting all non-aces

(3) getting at least one ace.

(4) Getting no red ace.

Answer #1

Number of aces in a deck = 4

Total number of cards in a deck = 52

Number of non aces = 52 - 4 = 48

Number of draws = 20

1) P(non ace) = 48/52 = 12/13

P(getting all non aces) = (12/13)20

= **0.2017**

2) P(not getting all non aces) = 1 - P(getting all non aces)

= 1 - 0.2017

= **0.7983**

3) P(getting at least one ace) = 1 - P(getting all non aces)

= **0.7983**

4) Number of red aces = 2

P(red ace) = 2/52 = 1/26

P(not a red ace) = 1 - 1/26 = 25/26

P(getting no red ace) = (25/26)20

= **0.4564**

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