Question 1026409: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.
How many hands contain 4 kings?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you draw 5 cards.
the probability that the first card will be a king is 4/52.
the probability that the second card will be a king is 3/51.
the probability that the third card will be a king is 2/50.
the probability that the fourth card will be a king is 1/49.
the probability that the fifth card will not be a king is 48/48.
this can occur 5c4 possible ways = 5 possible ways.
the probability is therefore 5 * 4 * 3 * 2 * 1 * 48 / (52 * 51 * 50 * 49 * 48).
this probability is equal to .00001846892603.
this means that, for every 54145 times you draw a hand of 5 cards from a full deck of 52 cards, you will get 1 hand that contains 4 kinds, on the average.
what does on the average mean?
it means that each set of 54145 times you draw, the number of hands won't be exactly 1 time for each set, but the overall average will be 1 or very close to it.
a small example:
first set of 54145 gets you 3 sets of hands with 4 kings.
second set of 54145 gets you 0 sets of hands with 4 kings.
third set of 54145 gets you 0 sets of hands with 4 kings.
the average is 3/3 = 1 hand with 4 kings in it for every 54145 times that you draw a hand of 5 cards.
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