Question

(1 point) 6 cards are drawn at random without replacement from a standard deck. Be accurate to 7 decimal places. a) Find the probability that all the cards are hearts. b) Find the probability that all the cards are face cards. Note: Face cards are kings, queens, and jacks. c) Find the probability that all the cards are even. (Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)

Answer 1

Answer:

a) P=0.0000843

b) P=0.0000454

c) P=0.0066113

Step-by-step explanation:

6 cards are drawn at random without replacement from a standard deck.

a) We calculate the probability that all the cards are hearts.

We calculatethe number of possible combinations:

$C^{52}_6=\frac{52!}{6!(52-6)!}=20358520$

We calculate the number of favorable combinations:

$C_6^{13}=\frac{13!}{6!(13-6)!}=1716$

Therefore, the probability is

$P=\frac{1716}{20358520}\\\\P=0.0000843$

b) We calculate the probability that all the cards are face cards.

We calculatethe number of possible combinations:

$C^{52}_6=\frac{52!}{6!(52-6)!}=20358520$

We calculate the number of favorable combinations:

$C_6^{12}=\frac{12!}{6!(12-6)!}=924$

Therefore, the probability is

$P=\frac{924}{20358520}\\\\P=0.0000454$

c) We calculate the probability that all the cards are even.

We calculatethe number of possible combinations:

$C^{52}_6=\frac{52!}{6!(52-6)!}=20358520$

We calculate the number of favorable combinations:

$C_6^{24}=\frac{24!}{6!(24-6)!}=134596$

Therefore, the probability is

$P=\frac{134596}{20358520}\\\\P=0.0066113$