4.119 Sports and Leisure Consider a regular 52-card deck of playing cards. Suppo

Question

4.119 Sports and Leisure Consider a regular 52-card deck of playing cards. Suppose two cards are drawn at random from a. What is the probability that the second card is an ace, b. What is the probability that the second card is an ace, c. What is the probability that the second card is a heart, d. Suppose two cards are drawn at random from the deck card is a heart, given that the first card is a heart? the deck without replacement. given that the first card is a king? given that the first card is an ace? given that the first card is a heart? with replacement. What is the probability that the second

Explanation / Answer

a) P(second card ace|first card king)=P(choosing one ace out of 4 from remaining 51 cards)=4/51

b)P(second card ace|frist card ace) =P(choosing one ace out of 3 from remaining 51 cards)=3/51 =1/17

c) P(second card heart|frist card heart)=12/51=4/17

d) P(second card heart|first card heart) =13/52 =1/4 (as experiment is done with replacement therefore again we have 13 card of hearts in a deck of 52)

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