Three students are playing a card game. They decide to choose the first person t

Question

Three students are playing a card game. They decide to choose the first person to play by each selecting a card from the 52-card deck and looking for the highest card in value and suit. They rank the suits from lowest to highest: clubs, dia- monds, hearts, and spades.
a. If the card is replaced in the deck after each student chooses, how many possible configurations of the three choices are possible?
b. How many configurations are there in which each student picks a different card?
c. What is the probability that all three students pick exactly the same card?
d. What is the probability that all three students pick different cards?

Explanation / Answer

since the cards are replaced after drawing, the number of cards remain at 52 for each draw qa 52*52*52 = 140,608 ------------- qb 52*51*50 = 132,600 -------------- qc first person can pick any card, each of the other two have to pick the same card from 52 P[all pick same card] = 1 *[1/52]^2 = 1/2704 ------------- qd first person can pick any card, each of the other two have to pick different cards P[all pick different cards] = 1*[51/52][50/52] = .9430 -----------

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