Q: A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?

$$\frac{4!}{2!2!} \times (0.5)^2$ \times (0.5)^2$

Q: Given the following probability distribution: $$P(0)=0.2$$, $$P(1)=0.5$$, $$P(2)=0.3$$, what is the mean $$\mu$$?

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

Q: For the same distribution as above, what is the variance $$\$$sigma^2$$?

$$(0-\mu)^2$ \times 0.2 + (1-\mu)^2$ \times 0.5 + (2-\mu)^2$ \times 0.3$$

Q: A binomial experiment has $$n=5$$ trials and $$p=0.4. $$What is the probability of getting exactly 3 successes?

$$\binom{5}{3} \times 0.4^3$ \times 0.6^2$

Question 1

A password consists of 3 letters followed by 2 digits. If each letter and digit can be used more than once, how many different passwords are possible?

Accepted Answer

$$26^3$$ 	imes $$10^2$$

Question 2

A table shows that 40 students are enrolled in Math, 30 in English, and 10 in both. What is the probability that a randomly selected student is enrolled in Math or English?

Accepted Answer

$$\frac{40+30-10}{60}$$

Question 3

In a hospital, 60% of patients are female. If 30% of all patients are female and over 60 years old, what is the probability that a randomly selected female patient is over 60?

Accepted Answer

$$\frac{0.3}{0.6}$$

Question 4

A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?

Accepted Answer

$$\frac{4!}{2!2!} 	imes (0.5)^2$ 	imes (0.5)^2$

Question 5

A card is drawn from a standard deck. What is the probability that it is a heart or a face card?

Accepted Answer

$$\frac{13}{52} + \frac{12}{52} - \frac{3}{52}$$

Question 6

How many ways can 5 books be arranged on a shelf?

Accepted Answer

$$5!$$

Question 7

A committee of 3 is to be chosen from 10 people. How many different committees are possible?

Accepted Answer

$$\binom{10}{3}$$

Question 8

A lottery ticket has 6 numbers chosen from 49. What is the probability of winning if only one combination wins?

Accepted Answer

$$\frac{1}{\binom{49}{6}}$$

Question 9

Which of the following is a continuous random variable?

Accepted Answer

The height of a randomly selected student

Question 10

Given the following probability distribution: $$P(0)=0.2$$, $$P(1)=0.5$$, $$P(2)=0.3$$, what is the mean $$\mu$$?

Accepted Answer

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

Question 11

For the same distribution as above, what is the variance $$\$$sigma^2$$?

Accepted Answer

$$(0-\mu)^2$ 	imes 0.2 + (1-\mu)^2$ 	imes 0.5 + (2-\mu)^2$ 	imes 0.3$$

Question 12

A binomial experiment has $$n=5$$ trials and $$p=0.4. $$What is the probability of getting exactly 3 successes?

Accepted Answer

$$\binom{5}{3} 	imes 0.4^3$ 	imes 0.6^2$

Question 13

For a binomial distribution with $$n=10$$ and $$p=0.2$$, what is the mean $$\mu$$?

Accepted Answer

$$10 	imes 0.2$$

Question 14

For the same binomial distribution ($$n=10$$, $$p=0.2$$), what is the variance $$\$$sigma^2$$?

Accepted Answer

$$10 	imes 0.2 	imes 0.8$$

Question 15

If $$P(E) = 0.7$$, what is $$P(E')$$?

Accepted Answer

$$1 - 0.7$$

Question 16

A normal distribution has mean $$\mu=50$$ and standard deviation $$\sigma=10. $$What is the $$z-$$score for $$x=70$$?

Accepted Answer

$$\frac{70-50}{10}$$

Question 17

If the probability of event $$A is$$ $$0.4$$ and the probability of event $$B$$ given $$A is$$ $$0.5$$, what is the probability of $$A$$ and $$B$$?

Accepted Answer

$$0.4 	imes 0.5$$

Question 18

A student scores a $$z-$$score of $$-1.5 on a $$test. What does this indicate?

Accepted Answer

The student scored 1.5 standard deviations below the mean

Question 19

A fair die is rolled 3 times. What is the probability of getting at least one six?

Accepted Answer

$$1 - (\frac{5}{6})^3$

Probability, Counting, and Discrete Distributions: Exam 2 Review Notes

Guida di studio - Domande di pratica

Study guide - Flashcard