Find the probabilities that a hand of 7 cards is drawn from well shuffled deck of 52 cards it contains 3 kings
Answers
Answer:
The probabilities of 52 carb are 3upon 52
Answer:
hey the answer is below :)
Step-by-step explanation:
(i) To find the probability that all the cards are kings:
If 7 cards are chosen from the pack of 52 cards
Then the total number of combinations possible are: 52C7
= 52!/[7! (52-7)!]
= 52!/ (7! 45!)
Assume that A be the event that all the kings are selected
We know that there are only 4 kings in the pack of 52 cards
Thus, if 7 cards are chosen, 4 kings are chosen out of 4, and 3 should be chosen form the 48 remaining cards.
Therefore, the total number of combinations is:
n(A) = 4C4 x48C3
= [4!/4!0! ] x [48!/3!(48-3)!]
= 1 x [48!/3! 45!]
= 48!/3! 45!
Therefore, P(A) = n(A)/n(S)
= [48!/3! 45!] ÷[52!/ (7! 45!]
= [48! x 7!] ÷ [3!x 52!]
= 1/7735
Therefore, the probability of getting all the 7 cards are kings is 1/7735
(ii) To find the probability that 3 cards are kings:
Assume that B be the event that 3 kings are selected.
Thus, if 7 cards are chosen, 3 kings are chosen out of 4, and 4 cards should be chosen form the 48 remaining cards.
Therefore, the total number of combinations is:
n(B) = 4C3 x48C4
= [4!/3!(4-3)! ] x [48!/4!(48-4)!]
= 4 x [48!/4! 44!]
= 48!/3! 45!
Therefore, P(B) = n(B)/n(S)
= [4 x48!/4! 44!] ÷[52!/ (7! 45!]
= 9/1547
Therefore, the probability of getting 3 kings is 9/1547
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