A poker hand consists of five cards randomly dealt from a standard deck of 52 ca
ID: 3123970 • Letter: A
Question
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.
Determine the probability that exactly 4 of these cards are Aces. Answer: %
Determine the probability that all five of these cards are Spades. Answer: %
Determine the probability that exactly 4 of these cards are face cards. Answer: %
Determine the probability of selecting exactly 2 Aces and exactly 2 Kings Answer: %
Determine the probability of selecting exactly 1 Jack. Answer: %
Explanation / Answer
The total number of combinations = 52C5 = 52*51*50*49*48/120 = 2598960
Determine the probability that exactly 4 of these cards are Aces.
Since four cards are aces, the fifth can come in 48 ways.
=> Probability = 48*100/2598960
Answer: 0.0018%
Determine the probability that all five of these cards are Spades.
Since they are all spades, they can come in 13C5 ways = 13*12*11*10*9/120 = 1287 ways.
=> Probability = 1287*100/2598960
Answer: 0.0495%
Determine the probability that exactly 4 of these cards are face cards.
There are 4*3 = 12 face cards.
The 4 face cards can be chosen in 12C4 ways = 12*11*10*9 / 24 = 495.
The remaining card can be any of the 40 non-face cards. So it can be chosen in 40 ways.
=> Probability = 495*40*100/2598960
Answer: 0.7618%
Determine the probability of selecting exactly 2 Aces and exactly 2 Kings
The 2 aces can be chosen in 4C2 ways. The 2 kings can be chosen in 4C2 ways. The last card can be any of the remaining 44.
So total combinations = 4C2 * 4C2 * 44 = 6*6*44 = 1584
=> Probability = 1584*100/2598960
Answer: 0.0609%
Determine the probability of selecting exactly 1 Jack.
The 1 jack can be chosen in 4 ways.
The remaining 4 cards can be chosen in 51C4 ways
= 51*50*49*48 / 24
= 249900
=> Probability = 4*249900*100/2598960
Answer: 38.46%
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