Download You must show all work and indicate the methods you use

AP Statistics
Probability Problems
1
You must show all work and indicate the methods you use. You will be graded on the
correctness of your methods and on the accuracy of your final answers.
1. A 4” x 4” x 4” cube is painted and then cut into sixty-four 1”x 1” x 1” cubes. A unit cube is
then randomly selected and rolled. What is the probability that the top face of the rolled cube
is painted? Express your answer as a common fraction.
2. In an El Nino year, the probability of spring drought in Cantonville is 60%. In a normal year,
it is 10 percent. In the next century, one-fifth of the years are expected to be El Nino years.
Find the expected number of drought years in Cantonville in the next century.
3. Diane challenges you to the following game. Roll two six-sided dice. If the product of the
two numbers is odd or divisible by 5, then you win; otherwise, Diane wins. Who has the
greater probability of winning? What is that probability (leave your answer as a common
fraction)?
4. A six-sided “loaded” die comes up ‘6’ one-fourth of the time and ‘1’ one-fourth of the time.
The other faces each come up one-eighth of the time. What is the probability of rolling a
sum of 7 using this trick die and a normal six-sided die?
5. Radio stations in the United States have call letters that begin with either K or W. Some
have a total of three letters, and others have four letters. How many different call-letter
combinations are possible?
1
AP Statistics
Probability Problems
2
You must show all work and indicate the methods you use. You will be graded on the
correctness of your methods and on the accuracy of your final answers.
1. Lisa has one red die and one green die, which she rolls to make up fractions. The green
die is the numerator, and the red die is the denominator. What is the probability of
rolling a fraction with a terminating decimal representation?
2. A survey of 50 students found that 30 had cats, 25 had dogs, 5 had white mice, 16 had
both dogs and cats, 4 had both dogs and mice, 2 had both cats and mice, and only 1 had
all three kinds of pets. How many students had no pets of these types?
3. If three quarters are tossed and if at least one lands tails up, what is the probability that at
least one lands heads up?
4. A pair of 8-sided dice has sides numbered 1 to 8. Each side has the same probability of
landing face up. What is the probability that the product of the two numbers on the sides
that face up exceeds 36?
5. When four fair coins are flipped, what is the probability of getting either exactly two
heads or exactly two tails?
2