You take the four Aces, four $2$'s, and four $3$'s from a standard deck of 52 cards, forming a set of $12$ cards. You then deal
all $12$ cards at random to four players, so that each player gets three cards. What is the probability that each player gets an Ace, a $2$, and a $3$?
1 answer:
Answer:
Probability each player gets an ace, a $2 and a $3 = 0.0374
Step-by-step explanation:
The total number of ways to divide the card in triples among four players = 369600 ways
The total number of ways to share the cards such that no card is repeated in each triple = 13824 ways
Probability each player gets an ace, a $2 and a $3 = 13824/369600
Probability each player gets an ace a $2 and a $3 = 0.0374
Note: Further explanation is provided in the attachment.
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a)
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b)
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Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
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Where and
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Part b
And we can find this probability using the complement rule, the normal standard table or excel and we got:
Part c
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.