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1. A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at
random from the box. What is the probability that both marbles are red?
a. 1/50
b. 1/60
c. 1/66
d. 1/24
e. 1/18
2. Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is
equally likely to pick any of the eight ice cream flavors. What is the probability that each child orders a different ice
cream type?
a. 5/72
b. 2/5
c. 7/64
d. 105/256
e. 45/128
3. Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange
each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and
two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the
following is the probability that the fruit is an apple?
a. .32
b. .4
c. .46
d. .5
e. .58
4. A media company plans to publish a special edition of a newspaper. Past experience shows that the number of
newspapers the company will sell is described by the following table:
Newspapers
210,000 to 220,001 to 230,001 to 240,001 to 250,001 to 260,001 to 270,001 to 280,001 to
220,000
230,000
240,000
250,000
260,000
270,000
280,000
290,000
Probability
.01
.07
.14
.25
.24
.15
.1
.04
a) What is the probability that the company will sell less than 250,000 newspapers?
b) The cost of selling this special edition is $100,000 for up to 260,000 newspapers and a flat cost of $10,000 if more
are sold. What is the expected sum the company will spend to sell the special edition?
c) Given that the company spends the flat extra cost of $10,000, what is the probability that the company sells
between $270,000 and $280,000 newspapers?
http://www.education.com/study-help/article/probability-random-variables-free-response-question/
http://www.free-test-online.com/ap/AP_Free_Response.html
http://www.free-test-online.com/ap/ap-statistics-multiple-choice.htm
5. Given that P(A) = 0.6, P(B) = 0.3, and P(B|A) = 0.5.
a.
P(A and B) = ?
b.
P(A or B) = ?
c.
Are events A and B independent? Explain.
6. Consider a set of 9000 scores on a national test that is known to be approximately normally distributed with a
mean of 500 and a standard deviation of 90.
a. What is the probability that a randomly selected student has a score greater than 600?
b. How many scores are there between 450 and 600?
c. Rachel needs to be in the top 1% of the scores on this test to qualify for a scholarship. What is the minimum
score Rachel needs?
7. Harvey, Laura, and Gina take turns throwing spit-wads at a target. Harvey hits the target 1/2 the time, Laura hits
it 1/3 of the time, and Gina hits the target 1/4 of the time. Given that somebody hit the target, what is the
probability that it was Laura?
8. Which of the following statements is (are) true of a normal distribution?
I.
II.
III.
Exactly 95% of the data are within two standard deviations of the mean.
The mean = the median = the mode.
The area under the normal curve between z = 1 and z = 2 is greater than the area between z = 2 and
z = 3.
9. The normal random variable X has a standard deviation of 12. We also know that P(x > 50) = 0.90. Find the mean
μ of the distribution.
10. Consider a random variable X with the following probability distribution:
a. Find P(X ≤ 22).
b. Find P(X > 21).
c. Find P(21 ≤ X < 24).
d. Find P(X ≤ 21 or X > 23).