Question 1

A bowl contains 12 poker chips: 3 red, 4 white, and 5 blue. If one chip is selected at random, what is the probability that it is not white?

Accepted Answer

$$\frac{7}{12}$$

Question 2

Two balanced dice are rolled. What is the probability that the sum of the dice is 7 or 11?

Accepted Answer

$$\frac{8}{36}$$

Question 3

According to the 2012 Russian presidential election data, what is the probability that a randomly selected voter voted for someone other than Putin?

Accepted Answer

$$\frac{21,173,824}{68,716,825}$$

Question 4

When one die is rolled, which outcomes constitute the event that the die comes up even?

Accepted Answer

$$\{2, 4, 6\}$$

Question 5

A World Series is selected at random. Let $$A be $$the event that the series was decided in four games, $$B$$ the event it was decided in less than six games, and $$C$$ the event it was decided in seven games. What is the number of outcomes for the event $$(A \cap B)$$?

Accepted Answer

21

Question 6

According to the age distribution of U.S. senators, what is the probability that a randomly selected senator is under 70 years old?

Accepted Answer

$$\frac{11 + 30 + 37}{100}$$

Question 7

Let $$X$$ denote the crew size of a randomly selected space shuttle mission. What is the probability that $$X = 4$$?

Accepted Answer

$$\frac{4}{144}$$

Question 8

When two balanced dice are rolled, what is the probability that the sum is 7?

Accepted Answer

$$\frac{6}{36}$$

Question 9

Given the probability distribution $$P(X=1)=0.3$$, $$P(X=2)=0.4$$, $$P(X=3)=0.3$$, what is the expected value (mean) of $$X$$?

Accepted Answer

$$2.0$$

Question 10

An American roulette wheel contains 38 numbers: 18 red, 18 black, and 2 green. If you bet $1 on red, what is the expected value of your winnings per play?

Accepted Answer

$$-0.052$$

Question 11

Find the area under the standard normal curve that lies to the right of $$z = -1.07.$$

Accepted Answer

$$0.8577$$

Question 12

A variable is normally distributed with mean $$68$$ and standard deviation $$10. $$What percentage of all possible values of the variable are at most $$90$$?

Accepted Answer

$$97.72\%$$

Question 13

A variable is normally distributed with mean $$6$$ and standard deviation $$2. $$What is the value that 65% of all possible values of the variable exceed?

Accepted Answer

$$4.62$$

Question 14

The times of finishers in the New York City 10-km run are normally distributed with mean $$61$$ minutes and standard deviation $$9$$ minutes. What percentage of finishers have times less than $$75$$ minutes?

Accepted Answer

$$93.32\%$$

Question 15

Umbilical cord pH for preterm infants is normally distributed with mean $$7.32$$ and standard deviation $$0.1. $$What percentage of infants have arterial cord pH levels between $$7.0$$ and $$7.5$$?

Accepted Answer

$$97.72\%$$

Question 16

Given the probability distribution for the sum $$Y of $$two dice: $$P(Y=2)=\frac{1}{36}$$, $$P(Y=3)=\frac{2}{36}$$, $$P(Y=4)=\frac{3}{36}$$, $$P(Y=5)=\frac{4}{36}$$, $$P(Y=6)=\frac{5}{36}$$, $$P(Y=7)=\frac{6}{36}$$, $$P(Y=8)=\frac{5}{36}$$, $$P(Y=9)=\frac{4}{36}$$, $$P(Y=10)=\frac{3}{36}$$, $$P(Y=11)=\frac{2}{36}$$, $$P(Y=12)=\frac{1}{36}$$, what is the mean (expected value) of $$Y$$?

Accepted Answer

$$7$$

Probability and Random Variables: Step-by-Step Guidance

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