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# 1.4: Review Questions

Difficulty Level: At Grade Created by: CK-12

Answer the following questions and show all work (including diagrams) to create a complete answer.

1. Determine which of the following are examples of independent events.
1. Rolling a 5 on one die and rolling a 5 on a second die.
2. Choosing a cookie from the cookie jar and choosing a jack from a deck of cards.
3. Winning a hockey game and scoring a goal.
2. Determine which of the following are examples of independent events.
1. Choosing an 8 from a deck of cards, replacing it, and choosing a face card.
2. Going to the beach and bringing an umbrella.
3. Getting gasoline for your car and getting diesel fuel for your car.
3. Determine which of the following are examples of dependent events.
1. Selecting a marble from a container and selecting a jack from a deck of cards.
2. Rolling a number less than 4 on a die and rolling a number that is even on the same roll.
3. Choosing a jack from a deck of cards and choosing another jack, without replacement.
4. Determine which of the following are examples of dependent events.
1. Selecting a book from the library and selecting a book that is a mystery novel.
2. Rolling a 2 on a die and flipping a coin to get tails.
3. Being lunchtime and eating a sandwich.
5. 2 dice are tossed. What is the probability of obtaining a sum equal to 6?
6. 2 dice are tossed. What is the probability of obtaining a sum less than 6?
7. 2 dice are tossed. What is the probability of obtaining a sum greater than 6?
8. 2 dice are tossed. What is the probability of obtaining a sum of at least 6?
9. A coin and a die are tossed. Calculate the probability of getting tails and a 5.
10. ABC\begin{align*}ABC\end{align*} High School is debating whether or not to write a policy where all students must have uniforms and wear them during school hours. In a survey, 45% of the students wanted uniforms, 35% did not, and 10% said they did not mind a uniform and did not care if there was no uniform. Represent this information in a Venn diagram.
11. ABC\begin{align*}ABC\end{align*} High School is debating whether or not to write a policy where all students must have uniforms and wear them during school hours. In a survey, 45% of the students wanted uniforms, and 55% did not. Represent this information in a Venn diagram.
12. For question 11, calculate the probability that a person selected at random from ABC\begin{align*}ABC\end{align*} High School will want the school to have uniforms or will not want the school to have uniforms.
13. Consider a sample set as S={2,4,6,8,10,12,14,16,18,20}\begin{align*}S = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}\end{align*}. Event A\begin{align*}A\end{align*} is the multiples of 4, while event B\begin{align*}B\end{align*} is the multiples of 5. What is the probability that a number chosen at random will be from both A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*}?
14. For question 13, what is the probability that a number chosen at random will be from either A\begin{align*}A\end{align*} or B\begin{align*}B\end{align*}?
15. Thomas bought a bag of jelly beans that contained 10 red jelly beans, 15 blue jelly beans, and 12 green jelly beans. What is the probability of Thomas reaching into the bag and pulling out a blue or green jelly bean?
16. Thomas bought a bag of jelly beans that contained 10 red jelly beans, 15 blue jelly beans, and 12 green jelly beans. What is the probability of Thomas reaching into the bag and pulling out a blue or green jelly bean and then reaching in again and pulling out a red jelly bean? Assume that the first jelly bean is not replaced.
17. Jack is a student in Bluenose High School. He noticed that a lot of the students in his math class were also in his chemistry class. In fact, of the 60 students in his grade, 28 students were in his math class, 32 students were in his chemistry class, and 15 students were in both his math class and his chemistry class. He decided to calculate what the probability was of selecting a student at random who was either in his math class or his chemistry class, but not both. Draw a Venn diagram and help Jack with his calculation.
18. Brenda did a survey of the students in her classes about whether they liked to get a candy bar or a new math pencil as their reward for positive behavior. She asked all 71 students she taught, and 32 said they would like a candy bar, 25 said they wanted a new pencil, and 4 said they wanted both. If Brenda were to select a student at random from her classes, what is the probability that the student chosen would want:
1. a candy bar or a pencil?
2. neither a candy bar nor a pencil?
19. A card is chosen at random from a standard deck of cards. What is the probability that the card chosen is a heart or spade? Are these events mutually exclusive?
20. A card is chosen at random from a standard deck of cards. What is the probability that the card chosen is a heart or a face card? Are these events mutually exclusive?

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