5. Many popular games are based on a standard deck of 52 playing cards. A face c

Question

5. Many popular games are based on a standard deck of 52 playing cards. A face card has a value and a suit. There are 13 face cards values: {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K} and each face card comes from one of 4 suits {Hearts, Diamonds, Clubs, Spades}. After shuffling two standards 52 card decks separately, one card is drawn from the first 52 deck is placed in the second deck. A card is then drawn randomly from the second deck. a. What is the probability that the second card is an Ace? b. Given that the second card drawn is an Ace, what is the conditional probability that an ace was transferred from the first deck of cards to the second?

Explanation / Answer

a)P(ace from second deck) =P(ace from first deck and ace from second deck+not ace from first and ace from second deck)

=(4/52)*(5/53)+(48/52)*(4/53) =212/2756 =53/689

b)conditional probability that an ace was transferred from the first deck of cards to the second given second card is ace =P(frist card ace|second card ace) =P(ace from first deck and ace from second deck)/P(second card ace)

=(4/52)*(5/53)/(53/689)=5/53

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