MATHEMATICS HIGH SCHOOL

Suppose you deal three cards from a regular deck of 52 cards, What is the probability that they will all be jacks?

Answers

Answer 1

Answer:

Answer:

$0.00018$

Step-by-step explanation:

The number of ways you can draw 3 cards from the deck of 52 cards is,

$\dbinom{52}{3}=(52!)/(3!\ 49!)=(52* 51* 50)/(6)=22100$

Out of 52, 4 cards are jacks. So the number of ways you can draw 3 jacks out of 4 is,

$\dbinom{4}{3}=(4!)/(3!\ 1!)=(24)/(6)=4$

So, the probability three cards from a regular deck of 52 cards will be,

$(4)/(22100)=0.00018$

Answer 2

Answer:

Final answer:

The likelihood of pulling three Jacks from a 52-card deck is calculated by multiplying together the probabilities of pulling a Jack on each of the three cards drawn. This comes to approximately 0.000181, or 0.0181%

Explanation:

The question you're asking is about the probability of drawing three Jacks from a 52-card deck. A standard deck has 52 cards, and there are 4 Jacks in the deck. So, when you're dealing the first card, the probability that it's a Jack is 4 out of 52, or 1 out of 13. After one Jack has been dealt, there are now only 3 Jacks left and 51 cards total, so the probability that the second card is a Jack is 3 out of 51. For the third card, because there are only 2 jacks left out of 50 cards, the probability is 2 out of 50. Because you want all these events to happen, you would multiply these probabilities together. Therefore, the probability of getting three Jacks is (4/52) * (3/51) * (2/50), which simplifies to approximately 0.000181.

Learn more about Probability here:

brainly.com/question/32117953

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What two numbers add to make 36 with one of the numbers being exactly twice the other? smaller number = and larger number =

Answers

Answer:

Smaller number = 12

Larger number = 24

Step-by-step explanation:

Let's call X the smallest number, while Y is the largest number.

In this case, Y = 2X

The equation that represents the given case is,

X + Y = 36

But being Y = 2X we substitute in the equation, obtaining ...

X + 2X = 36

Now we add the X ...

3X = 36

We isolate the X to know its value ...

$x=(36)/(3)$

X = 12

Now we calculate the value of Y ...

Y = 2X

Y = 2 (12)

Y = 24

Smaller number = 12

Larger number = 24

Both conditions are met:

(1) The largest number is twice the smallest number: 12 * 2 = 24

(2) The sum of the two numbers is 36: 12 + 24 = 36

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Hope this helps!

12 and 24
The equation is 2x + x =36
So 3x = 36
Then divide each side by 3
So x =12
That is the smaller number
Multiply it by 2 to get the bigger number since it's twice the number

A soup can has a height of 4 inches and a diameter of 3 inches. Which of the following is the closest to the volume of the soup can?

Answers

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(2, 8) and (3, 14)

Answers

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$\rm (y - y_2) = \left ((y_2 - y_1)/(x_2 - x_1) \right ) (x - x_2)$