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Ghella [55]
3 years ago
11

(1 point) 6 cards are drawn at random without replacement from a standard deck. Be accurate to 7 decimal places. a) Find the pro

bability 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)
Mathematics
1 answer:
V125BC [204]3 years ago
7 0

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

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b) see the picture attached

Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft

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if one paver has an area of----------------> 16/9 ft²
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<span>There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs.  After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”</span>

 

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