In this activity, you will use proportional relationships to predict how many times an event should occur for a certain number of trials. A standard deck of playing cards has four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, from ace to king. Use this information to answer the following questions.
Part A
What is the ratio of threes to the total number of cards in the deck?


part b Let x represent the number of times you’d expect a three to be drawn out of a total of 260 draws. Using the ratio from part A, write a proportion you can use to solve for x.

Part C
Solve the proportion you found in part B to determine the number of times you should expect a three to be drawn out of a total of 260 draws.

Part D
Is the answer that you got in part C an estimate or an exact number? Why?

Part E
How many times would a face card (jack, queen, or king) likely be drawn from the deck in 260 draws?

Part F
How many times would you expect a heart to be drawn in 260 draws from the deck?

Part G
Should you be surprised if a face card is drawn more times than a heart in 260 random draws? Why?

Answer: A 4/52        B X=260    C i dont know sorry

   D Yes, it did because the coordinates of the other polygons would be a direct opposite of polygon ABCD depending on what line it reflects off of. If it reflects off of the y-axis then they would be the same coordinates, just that the X values of the coordinates would now be positive, for the reflection of the x-axis it is also the same except that now the x value would now stay negative while the y values would now be positive. For y=x, it is different because now the X, and Y place values now switch (for example, (-3,-2) would now be (-2,-3)). For y=-x, the place values would both switch, and now be positive.          

E  The number of times a face card is expected to be drawn in 260 draws is 60 times.

F A 4/52 B X=260 D Yes, it did because the coordinates of the other polygons would be a direct opposite of polygon ABCD depending on what line it reflects off of. If it reflects off of the y-axis then they would be the same coordinates, just that the X values of the coordinates would now be positive, for the reflection of the x-axis it is also the same except that now the x value would now stay negative while the y values would now be positive. For y=x, it is different because now the X, and Y place values now switch (for example, (-3,-2) would now be (-2,-3)). For y=-x, the place values would both switch, and now be positive. E  The number of times a face card is expected to be drawn in 260 draws is 60 times. F 25 % Explanation: Assuming a random drawing from a standard pack of 52 cards: 1 4 = 25 % of the cards are hearts (i.e. 13 out of 52 ) G 25 % Explanation: Assuming a random drawing from a standard pack of 52 cards: 1 4 = 25 % of the cards are hearts (i.e. 13 out of 52 )    

G   How many face cards are there in a standard pack of 52 cards?

The deck has four suits: spades, clubs,hearts, and diamonds. Each suit has 3 face cards: king, queen and jack. So altogether there are 4 × 3 = 12 face cards in the 52-card deck.

There are different opinions about whether the ace is a picture card. Aces are not included in the answer.

The size of the sample space is 52. Assuming the cards are well-shuffled,

Pr(getting a face card when one card is drawn) = 1252=626=313

explanation : this took me forever

Part A:

The ratio of threes to the total number of cards in the deck is 1 : 13.

Part B:

1/13 = x/260

Part C:

The number of times you should expect a three to be drawn out of a total of 260 draws is 20.

Part D:

It is an estimate because the actual number of times a three is drawn in 260 draws may vary due to chance.

Part E:

We should expect a face card to be drawn approximately 60 times out of 260 draws.

Part F:

We should expect a heart to be drawn approximately 65 times out of 260 draws.

Part G:

We should not be surprised if a face card is drawn more times than a heart in 260 random draws.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Part A:

There are four threes in the deck and a total of 52 cards.

Therefore, the ratio of threes to the total number of cards in the deck is:

= Threes : Total number of cards

= 4 : 52

Simplifying the ratio by dividing both sides by 4 gives:

= Threes : Total number of cards

= 1 : 13

Part B:

Let x represent the number of times a three is expected to be drawn out of a total of 260 draws.

Using the ratio from part A, we can write the following proportion:

1/13 = x/260

Part C:

Solving the proportion from part B for x gives:

x = (1/13) x 260

x = 20

Therefore, we should expect a three to be drawn approximately 20 times out of 260 draws.

Part D:

The answer in part C is an estimate because the actual number of times a three is drawn in 260 draws may vary due to chance.

Part E:

There are 12 face cards in the deck (4 jacks, 4 queens, and 4 kings).

Using the ratio from part A, we can set up the following proportion:

4 x 12 / 52 = x / 260

Solving for x gives:

x = 60

Therefore, we should expect a face card to be drawn approximately 60 times out of 260 draws.

Part F:b

There are 13 hearts in the deck.

Using the ratio from part A, we can set up the following proportion:

13/52 = x/260

Solving for x gives:

x = 65

Therefore, we should expect a heart to be drawn approximately 65 times out of 260 draws.

Part G:

We should not be surprised if a face card is drawn more times than a heart in 260 random draws.

This is because there are more face cards in the deck (12) than hearts (13), and the proportion of face cards to the total number of cards is greater than the proportion of hearts to the total number of cards.

Thus,

All parts of the answer are mentioned above.

Learn more about expressions here:

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