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Evgesh-ka [11]
3 years ago
14

Se the following for problems 13 & 14. Three cards are drawn from a well-shuffled standard 52-card

Mathematics
1 answer:
frutty [35]3 years ago
5 0

Answer:

              \bold{(13)\ \dfrac{11}{1105}=0.1\%}\\\\\\\bold{(14)\ \dfrac{4}{8575}=0.05\%}

<u>Step-by-step explanation:</u>

(13)   Face cards are: Kings, Queens, and Jacks

There are 4 Kings, 4 Queens, and 4 Jacks in a standard deck of cards

1st\ card\qquad \times \qquad 2nd\ card\qquad \times \qquad 3rd\ card\\\\\dfrac{\text{12 K, Q, J's}}{\text{52 total cards}}\times\dfrac{\text{11 K, Q, J's}}{\text{51 remaining cards}}\times \dfrac{\text{10 K, Q, J's}}{\text{50 remaining cards}}\\\\\\=\dfrac{12\times 11\times 10}{52\times 51 \times 50}=\dfrac{1320}{132,600}=\large\boxed{\dfrac{11}{1105}}

(14)  There are 4 Aces and 4 Kings in a standard deck of cards

1st\ card\qquad \times \qquad 2nd\ card\qquad \times \qquad 3rd\ card\\\\\dfrac{\text{4 Aces}}{\text{52 total cards}}\times\dfrac{\text{4 Kings}}{\text{51 remaining cards}}\times \dfrac{\text{3 remaining Kings}}{\text{50 remaining cards}}\\\\\\=\dfrac{4\times 4\times 3}{52\times 51 \times 50}=\dfrac{48}{132,600}=\large\boxed{\dfrac{4}{8575}}

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