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ra1l [238]
3 years ago
13

If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

0.038 0.200 0.315 0.465 0.747
Mathematics
2 answers:
Svetradugi [14.3K]3 years ago
7 0
Last one..................................................................................................................................................

inysia [295]3 years ago
3 0

Answer:

The probability that exactly 2 of the cards are spades is 0.315  

Step-by-step explanation:

Given that 6 cards are drawn at random from a standard deck of 52 cards,

we have to find the probability that exactly 2 of the cards are spades.

Total cards=52

Number of cards which are spades=13

Remaining cards=52-13=39

Probability=\frac{\text{favourable outcomes}}{\text{Total number of outcomes}}

Probability=\frac{_2^{13}\txterm{C}\times _4^{39}\txterm{C}}{_6^{52}\txterm{C}}

Probability=\frac{\frac{13!}{2!11!}\times \frac{39!}{35!4!}}{\frac{52!}{6!46!}}=0.31512988174\sim 0.315

Option 3 is correct.

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A paper company needs to ship paper to a large printing business. The a paper will be
eimsori [14]

Given :

A paper company needs to ship paper to a large printing business.

The paper will be shipped in small boxes and large boxes.

Each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. A total of 19 boxes of paper were shipped weighing 1280 pounds altogether.

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Determine the number of small boxes shipped and the number of large boxes shipped.

Calculations :

Let "S" be small boxes and "L" be large boxes.

Small box + Large box = 19

50S + 80L = 1280

→ 5S + 8L = 128

→ 5 (19 - L) + 8L = 128

→ 3L = 128 - 95

→ L = 33/3

→ L = 11ㅤㅤ

Finding the small box:

→ S = 19 - L

→ S = 19 - 11

→ S = 8

Therefore ,

Large boxes = 11.

Small boxes = 8.

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The number of small boxes is 8 and that of the large boxes is 11.

Step-by-step explanation:

Each small box of paper weighs 50 pounds and each large box of paper

weighs 80 pounds. A total of 19 boxes of paper were shipped weighing 1280 pounds altogether.

Let there are x small boxes and y large boxes.

Then,

x + y = 19 ............ (1) and

50x + 80y = 1280

⇒ 5x + 8y = 128 ............... (2)

Now, solving equations (1) and (2) we get,

5( 19 - y) + 8y = 128

⇒ 3y = 128 - 95 = 33

⇒ y = 11

Now, from equation (1) we get, x = 19 - y = 19 - 11 = 8

Therefore, the number of small boxes is 8 and that of the large boxes is 11. (Answer)

8 0
2 years ago
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