Q: A spinner has 6 equal regions: 2 yellow, 2 blue, and 2 red. What is the probability of spinning yellow on the first spin and blue on the second spin?

$$\frac{2}{6} \times \frac{2}{6} = \frac{4}{36} = \frac{1}{9}$$

Q: A bag contains 2 red and 4 blue marbles. If you draw one marble, keep it, and then draw another, what is the probability that both are blue?

$$\frac{4}{6} \times \frac{3}{5} = \frac{12}{30} = \frac{2}{5}$$

Question 1

Which of the following best describes the difference between theoretical and empirical probability?

Accepted Answer

Theoretical probability is based on what could happen, while empirical probability is based on what actually did happen.

Question 2

A bag contains 3 red marbles and 5 blue marbles. If you draw one marble at random, what is the probability that it is red? Express your answer as a reduced fraction.

Accepted Answer

$$\frac{3}{8}$$

Question 3

If $$P(A) = 0.3$$, what is the probability of the complement of event $$A$$?

Accepted Answer

$$0.7$$

Question 4

A weather report states there is a 20% chance of rain and a 30% chance of snow tomorrow. What is the probability that it will NOT rain or snow?

Accepted Answer

$$0.5$$

Question 5

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Rolling a 2 and rolling a 5 on a single six-sided die.

Question 6

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ for mutually exclusive events $$A$$ and $$B$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 7

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?

Accepted Answer

$$\frac{16}{52}$$

Question 8

If two events $$A$$ and $$B$$ are independent, which formula correctly gives the probability that both occur?

Accepted Answer

$$P(A \cap B) = P(A) \cdot P(B)$$

Question 9

A spinner has 6 equal regions: 2 yellow, 2 blue, and 2 red. What is the probability of spinning yellow on the first spin and blue on the second spin?

Accepted Answer

$$\frac{2}{6} 	imes \frac{2}{6} = \frac{4}{36} = \frac{1}{9}$$

Question 10

Given the contingency table below, what is the probability that a randomly selected student is a senior and drives a car?

|         | Drives a Car | Does Not Drive a Car | Total |
|---------|--------------|---------------------|-------|
| Senior  |     40       |         10          |  50   |
| Junior  |     20       |         30          |  50   |
| Total   |     60       |         40          | 100   |

Accepted Answer

$$\frac{40}{100}$$

Question 11

A bag contains 2 red and 4 blue marbles. If you draw one marble, keep it, and then draw another, what is the probability that both are blue?

Accepted Answer

$$\frac{4}{6} 	imes \frac{3}{5} = \frac{12}{30} = \frac{2}{5}$$

Question 12

In a town, 15% of people have both a cat and a dog, and 64% have a dog. What is the probability that a randomly selected person has a cat, given they have a dog?

Accepted Answer

$$\frac{0.15}{0.64}$$

Question 13

A rare disease affects 1 out of every 100 people. The test for this disease is correct 95% of the time if the person has the disease, and gives a false positive 10% of the time if the person does not have the disease. What is $$P(A|B)$$, where $$A is$$ 'tested positive' and $$B is$$ 'has the disease'?

Accepted Answer

$$0.95$$

Question 14

How many different ways can you arrange the letters in the word 'BANANA'?

Accepted Answer

$$\frac{6!}{3!2!}$$

Question 15

A teacher is choosing a president, vice president, and treasurer from a club with 13 members. How many ways can these positions be filled?

Accepted Answer

$$13 	imes 12 	imes 11$$

Question 16

An ice cream shop has 32 flavors. You need to pick 2 flavors to blend into a milkshake. How many possible ways can you select your flavors?

Accepted Answer

$$\frac{32!}{2!30!}$$

Question 17

When rolling two six-sided dice, what is the probability that both show a 6?

Accepted Answer

$$\frac{1}{36}$$

Question 18

A lottery game requires you to choose 5 numbers between 1 and 40. What is the probability of winning if you buy one ticket?

Accepted Answer

$$\frac{1}{\binom{40}{5}}$$

Introductory Probability Concepts and Counting Principles

Guida di studio - Domande di pratica

Study guide - Flashcard