Q: A bag contains 3 red, 2 blue, and 5 green marbles. If you draw one marble, replace it, and then draw another, what is the probability that both marbles are blue?

$$\frac{2}{10} \times \frac{2}{10} = \frac{4}{100}$$

Q: A probability distribution is given by $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the mean $$\mu of $$this distribution?

$$0 \times 0.2 + 1 \times 0.5 + 2 \times 0.3 = 1.1$$

Q: A medical test for a disease has a 95% chance of correctly identifying a diseased person (true positive) and a 90% chance of correctly identifying a healthy person (true negative). If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

$$0.01 \times 0.95 + 0.99 \times 0.10 = 0.1085$$

Question 1

A weather forecaster estimates a 70% chance of rain tomorrow based on her experience and current weather patterns. What type of probability is this?

Accepted Answer

Subjective probability

Question 2

Which of the following is a simple event when rolling a standard six-sided die?

Accepted Answer

Rolling a 3

Question 3

Suppose you draw two cards from a standard deck of 52 cards, one after the other, without replacement. Are these two events independent or dependent?

Accepted Answer

Dependent, because the outcome of the first draw affects the probability of the second

Question 4

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Rolling a 2 and rolling a 5 on a single die

Question 5

A password consists of 4 different letters chosen from the English alphabet. In how many ways can the password be arranged if the order matters?

Accepted Answer

$$\frac{26!}{22!}$$

Question 6

Which of the following is a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour

Question 7

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

Each outcome must be equally likely

Question 8

A factory tests 10 light bulbs and records the number of defective bulbs. Is this experiment binomial?

Accepted Answer

Yes, because each bulb is either defective or not, and the probability of defect is the same for each bulb

Question 9

Given $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 10

If the probability of an event is $$0.03$$, is this event considered unusual?

Accepted Answer

Yes, because it is less than $$0.05$$

Question 11

A bag contains 3 red, 2 blue, and 5 green marbles. If you draw one marble, replace it, and then draw another, what is the probability that both marbles are blue?

Accepted Answer

$$\frac{2}{10} 	imes \frac{2}{10} = \frac{4}{100}$$

Question 12

A committee of 4 is to be chosen from 10 people. How many different committees can be formed?

Accepted Answer

$$\binom{10}{4}$$

Question 13

A probability distribution is given by $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the mean $$\mu of $$this distribution?

Accepted Answer

$$0 	imes 0.2 + 1 	imes 0.5 + 2 	imes 0.3 = 1.1$$

Question 14

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

$$\binom{5}{3} \left(\frac{1}{2}\$$right)^3$$ \left(\frac{1}{2}\$$right)^2$$

Question 15

A medical test for a disease has a 95% chance of correctly identifying a diseased person (true positive) and a 90% chance of correctly identifying a healthy person (true negative). If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.01 	imes 0.95 + 0.99 	imes 0.10 = 0.1085$$

Question 16

If $$P(A|B) = 0.4$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Question 17

A tree diagram is used to represent the possible outcomes of flipping a coin twice. What is the probability of getting at least one head?

Accepted Answer

$$1 - \frac{1}{4} = \frac{3}{4}$$

Question 18

Which calculator function would you use to find the number of ways to arrange 7 books on a shelf?

Accepted Answer

$$7!$$

Question 19

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the standard deviation $$\sigma of$$ $$X$$?

Accepted Answer

$$\sqrt{0.2(1-2.1)^2$ + 0.5(2-2.1)^2$ + 0.3(3-2.1)^2$}$$

Study Guide: Probability and Discrete Probability Distributions (Chapters 3 & 4)

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