Statistics and probability worksheet using playing cards to teach probability concepts.

Here are the solutions to the probability problems. I have worked through each one step-by-step to ensure accuracy.

Key Information for a Standard Deck of Cards:
* Total cards: 52
* Suits: Hearts, Diamonds, Clubs, Spades (13 cards in each suit).
* Ranks: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace (4 of each rank).
* Red cards: Hearts and Diamonds (26 total).
* Black cards: Clubs and Spades (26 total).
* Face cards: Jacks, Queens, Kings (12 total: 3 per suit × 4 suits).

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Step-by-Step Solutions

1) Drawing a 6 from a deck of cards?
* There are four 6s in a deck (6 of Hearts, 6 of Diamonds, 6 of Clubs, 6 of Spades).
* Total cards = 52.
* Probability = $4/52$.
* Simplified: Divide top and bottom by 4 $\rightarrow$ $1/13$.

2) Drawing 2 cards that are all spades from a deck of cards?
* First card is a spade: There are 13 spades out of 52 cards ($13/52 = 1/4$).
* Second card is a spade: Now there are 12 spades left out of 51 cards ($12/51$).
* Multiply them: $(1/4) \times (12/51) = 12/204$.
* Simplified: Divide by 12 $\rightarrow$ $1/17$.

3) Drawing a black card from a deck of cards?
* Black cards are Clubs and Spades. $13 + 13 = 26$ black cards.
* Probability = $26/52$.
* Simplified: $1/2$.

4) Rolling an odd number on a die?
* A standard die has numbers 1, 2, 3, 4, 5, 6.
* Odd numbers are 1, 3, 5. That is 3 numbers.
* Total outcomes = 6.
* Probability = $3/6$.
* Simplified: $1/2$.

5) Drawing a 3 from a deck of cards?
* There are four 3s in a deck.
* Probability = $4/52$.
* Simplified: $1/13$.

6) Drawing a club from a deck of cards?
* There are 13 clubs in a deck.
* Probability = $13/52$.
* Simplified: $1/4$.

7) Drawing 2 cards that are all 8 from a deck of cards?
* First card is an 8: There are four 8s out of 52 cards ($4/52 = 1/13$).
* Second card is an 8: Now there are three 8s left out of 51 cards ($3/51 = 1/17$).
* Multiply them: $(1/13) \times (1/17) = 1/221$.
* Answer: $1/221$.

8) Drawing a heart from a deck of cards?
* There are 13 hearts in a deck.
* Probability = $13/52$.
* Simplified: $1/4$.

9) Drawing a 7 from a deck of cards?
* There are four 7s in a deck.
* Probability = $4/52$.
* Simplified: $1/13$.

10) Drawing 2 cards that are at 2 from a deck of cards?
*(Note: "at 2" likely means "are 2s")*
* First card is a 2: There are four 2s out of 52 cards ($4/52 = 1/13$).
* Second card is a 2: Now there are three 2s left out of 51 cards ($3/51 = 1/17$).
* Multiply them: $(1/13) \times (1/17) = 1/221$.
* Answer: $1/221$.

11) Rolling an even number on a die?
* Even numbers on a die are 2, 4, 6. That is 3 numbers.
* Total outcomes = 6.
* Probability = $3/6$.
* Simplified: $1/2$.

12) Drawing 2 cards that are all 9 from a deck of cards?
* First card is a 9: There are four 9s out of 52 cards ($4/52 = 1/13$).
* Second card is a 9: Now there are three 9s left out of 51 cards ($3/51 = 1/17$).
* Multiply them: $(1/13) \times (1/17) = 1/221$.
* Answer: $1/221$.

13) Drawing a red card from a deck of cards?
* Red cards are Hearts and Diamonds. $13 + 13 = 26$ red cards.
* Probability = $26/52$.
* Simplified: $1/2$.

14) Rolling a 1 on a die?
* There is only one "1" on a die.
* Total outcomes = 6.
* Probability: $1/6$.

15) Drawing a face card from a deck of cards?
* Face cards are Jacks, Queens, and Kings.
* There are 3 face cards per suit $\times$ 4 suits = 12 face cards.
* Probability = $12/52$.
* Simplified: Divide by 4 $\rightarrow$ $3/13$.

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Final Answer:
1) 1/13
2) 1/17
3) 1/2
4) 1/2
5) 1/13
6) 1/4
7) 1/221
8) 1/4
9) 1/13
10) 1/221
11) 1/2
12) 1/221
13) 1/2
14) 1/6
15) 3/13