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# Probability and Statistics

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Two cards are drawn at random from a deck of cards. (write all the answers to 4 decimal places)

(a)        What is the probability that both cards are aces if the first card is put back into the deck (which is then shuffled) before the second card is drawn?

(b)       What is the probability that both cards are aces if the first card is not put back into the deck (drawing without replacement)?

Sep 29, 2017

### 1+0 Answers

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(a)        What is the probability that both cards are aces if the first card is put back into the deck (which is then shuffled) before the second card is drawn?

P (ace on the first draw  = 4/52    = 1/13

P (ace on the second draw)  = 4/52   = 1/13

P(ace on both draws)  = (1/13) (1/13)  ≈  .0059

(b)       What is the probability that both cards are aces if the first card is not put back into the deck (drawing without replacement)?

P (ace on the first draw  = 4/52    = 1/13

P (ace on the second draw)  = 3/51   = 1/17

P(ace on both draws)  = (1/13) (1/17)  ≈  .0045   Sep 29, 2017