Question

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

deck of playing cards.
13. Find the probability that all three cards are face cards.
14. Find the probability that the first card is an ace and the last two cards are kings.
Blood types can be classified as either Rh or Rh. According to the Information Please Almanac, 99%
of the Chinese population has Rh blood.
15. What is the probability that six randomly selected Chinese people have Rh blood?
16. What is the probability that at least one of the six randomly selected Chinese people has Rh
blood?

Answer 1

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

Explanation:

(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 * \qquad 2nd\ card\qquad * \qquad 3rd\ card\\\\\frac{\text{12 K, Q, J's}}{\text{52 total cards}}*\frac{\text{11 K, Q, J's}}{\text{51 remaining cards}}* \frac{\text{10 K, Q, J's}}{\text{50 remaining cards}}\\\\\\=(12* 11* 10)/(52* 51 * 50)=(1320)/(132,600)=\large\boxed{(11)/(1105)}`

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

`1st\ card\qquad * \qquad 2nd\ card\qquad * \qquad 3rd\ card\\\\\frac{\text{4 Aces}}{\text{52 total cards}}*\frac{\text{4 Kings}}{\text{51 remaining cards}}* \frac{\text{3 remaining Kings}}{\text{50 remaining cards}}\\\\\\=(4* 4* 3)/(52* 51 * 50)=(48)/(132,600)=\large\boxed{(4)/(8575)}`