Q: A license plate consists of 6 characters: the first three are letters (first letter not 'O'), the last three are numbers (last digit not 0). How many possible license plates are there?

$$25 \times 26 \times 26 \times 10 \times 10 \times 9$$

Q: In a group of 10 students, 8 pass a class. If you select two students at random without replacement, what is the probability that both pass?

$$\frac{8}{10} \times \frac{7}{9}$$

Q: Given the probability distribution for the number of games played in the World Series (1903–2017): $$P(4)=0.194$$, $$P(5)=0.231$$, $$P(6)=0.222$$, $$P(7)=0.370$$, $$P(8)=0.028. $$What is the expected value (mean) of the number of games played?

$$4 \times 0.194 + 5 \times 0.231 + 6 \times 0.222 + 7 \times 0.370 + 8 \times 0.028$$

Q: For a binomial distribution with $$n=8$$ and $$p=\frac{1}{5}$$, what is the expected number of questions you get correct?

$$n \times p = 8 \times \frac{1}{5} = 1.6$$

Q: In a binomial experiment with $$n=8$$ and $$p=\frac{1}{5}$$, what is the variance?

$$n \times p \times q = 8 \times \frac{1}{5} \times \frac{4}{5}$$

Question 1

A computer randomly selects a number between 1 and 1000. What is the probability that the number is even?

Accepted Answer

$$\frac{500}{1000}$$

Question 2

A new McDonald’s meal deal allows you to select from 3 sides, 8 entrees, and 4 desserts. How many unique meals can be formed?

Accepted Answer

$$3 	imes 8 	imes 4 = 96$$

Question 3

What is the probability of rolling a six-sided die and getting an even number?

Accepted Answer

$$\frac{3}{6} = \frac{1}{2}$$

Question 4

There is an 80% chance that a student will remember to bring a formula sheet to class. What is the probability that the student will forget?

Accepted Answer

$$1 - 0.80 = 0.20$$

Question 5

A Lighthouse ID consists of 6 digits past the A00 start. What is the probability that you randomly guess the correct Lighthouse ID?

Accepted Answer

$$\frac{1}{10^6$}$$

Question 6

A license plate consists of 6 characters: the first three are letters (first letter not 'O'), the last three are numbers (last digit not 0). How many possible license plates are there?

Accepted Answer

$$25 	imes 26 	imes 26 	imes 10 	imes 10 	imes 9$$

Question 7

In a group of 10 students, 8 pass a class. If you select two students at random without replacement, what is the probability that both pass?

Accepted Answer

$$\frac{8}{10} 	imes \frac{7}{9}$$

Question 8

A study found that 85% of Floridians think the home insurance system has major defects. Of these, 6 out of 10 feel the system can be fixed. What is the probability a person feels the system has major defects AND can be fixed?

Accepted Answer

$$0.85 	imes 0.6 = 0.51$$

Question 9

A card is selected at random from a standard 52-card deck. What is the probability of selecting a queen and a red card?

Accepted Answer

$$\frac{2}{52}$$

Question 10

In a three-child family, the probability of having two girls is 0.375. What is the probability of selecting a family with at least two girls?

Accepted Answer

$$0.375 + 0.125 = 0.5$$

Question 11

Is the number of videos rented in a one-month period discrete or continuous?

Accepted Answer

Discrete

Question 12

Given the probability distribution for the number of games played in the World Series (1903–2017): $$P(4)=0.194$$, $$P(5)=0.231$$, $$P(6)=0.222$$, $$P(7)=0.370$$, $$P(8)=0.028. $$What is the expected value (mean) of the number of games played?

Accepted Answer

$$4 	imes 0.194 + 5 	imes 0.231 + 6 	imes 0.222 + 7 	imes 0.370 + 8 	imes 0.028$$

Question 13

You are taking an 8-question multiple choice test (with 5 choices per question). What is the probability of guessing exactly 3 questions correctly?

Accepted Answer

$$\binom{8}{3} \left(\frac{1}{5}\$$right)^3$$ \left(\frac{4}{5}\$$right)^5$$

Question 14

Which of the following is NOT a binomial experiment?

Accepted Answer

Play a ring toss game until you win, with a chance of 0.3 of winning each game.

Question 15

In a group of 50 apartment residents, what is the probability that a randomly chosen resident is a female given that the person is a college student? (Given: 13 female college students, 26 total college students)

Accepted Answer

$$\frac{13}{26}$$

Question 16

For a binomial distribution with $$n=8$$ and $$p=\frac{1}{5}$$, what is the expected number of questions you get correct?

Accepted Answer

$$n 	imes p = 8 	imes \frac{1}{5} = 1.6$$

Question 17

In a binomial experiment with $$n=8$$ and $$p=\frac{1}{5}$$, what is the variance?

Accepted Answer

$$n 	imes p 	imes q = 8 	imes \frac{1}{5} 	imes \frac{4}{5}$$

Question 18

A card is selected at random from a standard 52-card deck. What is the probability of selecting a diamond or a black card?

Accepted Answer

$$\frac{26 + 13}{52} = \frac{39}{52}$$

Question 19

In a probability distribution, the standard deviation is calculated as:

Accepted Answer

$$\sqrt{\sum (x - \mu)^2$ P(x)}$$

STA 2023 Test 2 Practice – Step-by-Step Statistics Guidance

Study Guide - Practice Questions

Study Guide - Flashcards