Answers in bold:
- 14. probability = 2/13 (choice D)
- 15. probability = 4/663 (choice C)
- 16. probability = 3/52 (choice B)
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Explanation for problem 14
There are 4 aces and 4 copies of "9".
4+4 = 8 cards we want to select out of 52 total
8/52 = (4*2)/(4*13) = 2/13 which points to choice D as the final answer
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Explanation for problem 15
4 kings gives a probability of 4/52 = 1/13.
After the king is chosen, there are 52-1 = 51 cards left since we aren't replacing it. The probability of getting a queen on the second selection is 4/51
(1/13)*(4/51) = 4/663 is the probability of a king, then a queen, with no replacement. We arrive at choice C as the final answer.
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Explanation for problem 16
face card = picture card
face card = Jack, Queen, King
aces are not considered a face card
3*4 = 12 face cards in total
A = 12/52 = (4*3)/(4*13) = 3/13 is the probability of selecting a face card.
That card is then put back (aka replacement) and we still have 52 cards in the deck. We don't drop down to 51.
13 hearts ---> B = 13/52 = 1/4 is the probability of getting a heart
A*B = (3/13)*(1/4) = 3/52 is the probability of getting a face card, then a heart, when replacement is done. The final answer is choice B