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# Probability and Random Variables Multiple Choice Practice Problems for AP Statistics

based on 3 ratings
By — McGraw-Hill Professional
Updated on Feb 3, 2011

Review the following concepts if necessary:

### Problems

1. In the table above what are P(A and E ) and P(C | E )?

1. 12/125, 28/125
2. 12/63, 28/60
3. 12/125, 28/63
4. 12/125, 28/60
5. 12/63, 28/63
2. For the tree diagram pictured above, what is P(B | X )?

1. 1/4
2. 5/17
3. 2/5
4. 1/3
5. 4/5
3. It turns out that 25 seniors at Fashionable High School took both the AP Statistics exam and the AP Spanish Language exam. The mean score on the Statistics exam for the 25 seniors was 2.4 with a standard deviation of 0.6 and the mean score on the Spanish Language exam was 2.65 with a standard deviation of 0.55. We want to combine the scores into a single score. What are the correct mean and standard deviation of the combined scores?
1. 5.05; 1.15
2. 5.05; 1.07
3. 5.05; 0.66
4. 5.05; 0.81
5. 5.05; you cannot determine the standard deviation from this information.
4. The GPA (grade point average) of students who take the AP Statistics exam are approximately normally distributed with a mean of 3.4 with a standard deviation of 0.3. Using Table A, what is the probability that a student selected at random from this group has a GPA lower than 3.0?
1. 0.0918
2. 0.4082
3. 0.9082
4. –0.0918
5. 0
5. The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows: White: 46%, Latino: 32%, Asian: 11%, Black: 7%, and Other: 4%. Assuming that these are mutually exclusive categories (this is not a realistic assumption, especially in California), what is the probability that a random selected person from the state of California is of Asian or Latino descent?
1. 46%
2. 32%
3. 11%
4. 43%
5. 3.5%
6. The students in problem #4 above were normally distributed with a mean GPA of 3.4 and a standard deviation of 0.3. In order to qualify for the school honor society, a student must have a GPA in the top 5% of all GPAs. Accurate to two decimal places, what is the minimum GPA Norma must have in order to qualify for the honor society?
1. 3.95
2. 3.92
3. 3.75
4. 3.85
5. 3.89
7. The following are the probability distributions for two random variables, X and Y:
8. If X and Y are independent, what is P(X = 5 and Y = 4)?

9. The following table gives the probabilities of various outcomes for a gambling game.
10. What is the player's expected return on a bet of \$1?

1. \$0.05
2. –\$0.60
3. –\$0.05
4. –\$0.10
5. You can't answer this question since this is not a complete probability distribution.
11. You own an unusual die. Three faces are marked with the letter "X," two faces with the letter "Y," and one face with the letter "Z." What is the probability that at least one of the first two rolls is a "Y"?
12. You roll two dice. What is the probability that the sum is 6 given that one die shows a 4?

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