Probability worksheet with six math problems involving chance and odds.

Let's solve each problem step by step:

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Problem 1:

Question: If you roll a die, what are the chances of rolling a 2?

Solution:
- A standard die has 6 faces, numbered 1 through 6.
- Each face is equally likely to appear when the die is rolled.
- There is only 1 favorable outcome (rolling a 2).
- The total number of possible outcomes is 6.

The probability of rolling a 2 is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6}
\]

Answer: $\boxed{\frac{1}{6}}$

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Problem 2:

Question: If you roll a die, what is the probability that you will roll an even number?

Solution:
- The numbers on a die are: 1, 2, 3, 4, 5, 6.
- The even numbers among these are: 2, 4, 6.
- There are 3 favorable outcomes (rolling a 2, 4, or 6).
- The total number of possible outcomes is 6.

The probability of rolling an even number is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{6} = \frac{1}{2}
\]

Answer: $\boxed{\frac{1}{2}}$

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Problem 3:

Question: A bag contains 3 red marbles, 3 blue marbles, and 4 green marbles. If a marble is drawn from the bag at random, what is the probability that the marble will be blue?

Solution:
- Total number of marbles in the bag:
\[
3 \text{ (red)} + 3 \text{ (blue)} + 4 \text{ (green)} = 10
\]
- Number of favorable outcomes (drawing a blue marble): 3
- Total number of possible outcomes: 10

The probability of drawing a blue marble is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{10}
\]

Answer: $\boxed{\frac{3}{10}}$

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Problem 4:

Question: A bag contains 6 number files. The numbers on the files are 3, 7, 8, 9, 13, and 15. If you randomly draw one file from the bag, what is the probability of picking an odd number?

Solution:
- List the numbers on the files: 3, 7, 8, 9, 13, 15.
- Identify the odd numbers: 3, 7, 9, 13, 15.
- There are 5 odd numbers.
- Total number of possible outcomes: 6.

The probability of picking an odd number is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{6}
\]

Answer: $\boxed{\frac{5}{6}}$

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Problem 5:

Question: Mr. Jones has a hard time believing because the basket ball team he coaches has five girls and four boys. Because the basketball team has too many players to go to a charity event with him, Mary, Carla, John, Lynda, Feike, and Janessa all want to go. They each write their name on a piece of paper and put it in a hat. Mr. Jones randomly selects one child to go with him. What is the probability that he will select a boy? What is the probability that he will select a girl?

Solution:
- Total number of children: 5 girls + 4 boys = 9 children.
- Number of favorable outcomes for selecting a boy: 4.
- Number of favorable outcomes for selecting a girl: 5.

#### Probability of selecting a boy:
\[
\text{Probability (boy)} = \frac{\text{Number of boys}}{\text{Total number of children}} = \frac{4}{9}
\]

#### Probability of selecting a girl:
\[
\text{Probability (girl)} = \frac{\text{Number of girls}}{\text{Total number of children}} = \frac{5}{9}
\]

Answers:
- Probability of selecting a boy: $\boxed{\frac{4}{9}}$
- Probability of selecting a girl: $\boxed{\frac{5}{9}}$

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Problem 6:

Question: John and Jackie are rolling a die. John wins if he rolls a number higher than 4. Jackie wins if the number rolled is 4 or less. Is this game fair? Explain.

Solution:
- A standard die has 6 faces: 1, 2, 3, 4, 5, 6.
- John wins if the number rolled is higher than 4: This means the favorable outcomes for John are 5 and 6. There are 2 favorable outcomes.
- Jackie wins if the number rolled is 4 or less: This means the favorable outcomes for Jackie are 1, 2, 3, and 4. There are 4 favorable outcomes.

#### Probability of John winning:
\[
\text{Probability (John wins)} = \frac{\text{Number of favorable outcomes for John}}{\text{Total number of possible outcomes}} = \frac{2}{6} = \frac{1}{3}
\]

#### Probability of Jackie winning:
\[
\text{Probability (Jackie wins)} = \frac{\text{Number of favorable outcomes for Jackie}}{\text{Total number of possible outcomes}} = \frac{4}{6} = \frac{2}{3}
\]

Since the probabilities of John winning ($\frac{1}{3}$) and Jackie winning ($\frac{2}{3}$) are not equal, the game is not fair. Jackie has a higher chance of winning.

Answer: No, the game is not fair. Jackie has a higher probability of winning ($\frac{2}{3}$) compared to John ($\frac{1}{3}$).

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Final Answers:

1. $\boxed{\frac{1}{6}}$
2. $\boxed{\frac{1}{2}}$
3. $\boxed{\frac{3}{10}}$
4. $\boxed{\frac{5}{6}}$
5. Probability of selecting a boy: $\boxed{\frac{4}{9}}$, Probability of selecting a girl: $\boxed{\frac{5}{9}}$
6. $\boxed{\text{No, the game is not fair.}}$