Q: If two people are chosen at random from a group of 350 people, 97 of whom have blue eyes, what is the probability that neither person has blue eyes?

$$\frac{253}{350} \times \frac{252}{349} = 0.522$$

Q: From a pool of 30 qualified Starfleet Officers, how many ways can you fill the positions of Captain, First Officer, Science Officer, and Chief Security Officer (order matters)?

$$30 \times 29 \times 28 \times 27 = 657,720$$

Q: The probability that a Jedi trained by Obiwan Kenobi will go to the Dark Side is 0.07. If Master Kenobi trains 7 apprentices, what is the probability that exactly 2 of them will turn to the Dark Side?

$$\binom{7}{2} \times 0.07^2$ \times 0.93^5$ = 0.0716$$

Question 1

Which of the following values is a valid probability for a single event, and why?

Accepted Answer

0.32% because probabilities must be between 0 and 1, and 0.32% is less than 1.

Question 2

If a regular six-sided die is rolled, what is the probability of rolling an odd number?

Accepted Answer

$$\frac{3}{6} = 0.5$$

Question 3

Two events are said to be independent if:

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 4

Which of the following random variables is continuous?

Accepted Answer

The amount of time a dog spends in a dog park in a day.

Question 5

A probability distribution is valid if:

Accepted Answer

All probabilities are between 0 and 1, and the sum of all probabilities equals 1.

Question 6

If you toss a coin and then roll a 6-sided die, how many possible outcomes are there?

Accepted Answer

$$2 	imes 6 = 12$$

Question 7

In a survey, 827 students prefer X-Box 360 and 673 prefer PlayStation 3. What is the probability that a randomly selected student prefers X-Box 360?

Accepted Answer

$$\frac{827}{827+673} = 0.551$$

Question 8

Given the following table, what is the probability that a randomly selected student is a sophomore given that they do NOT carry a credit card?

Freshman: 16 carry, 21 do not
Sophomore: 57 carry, 6 do not
Total: 73 carry, 27 do not

Accepted Answer

$$\frac{6}{27} = 0.222$$

Question 9

If two people are chosen at random from a group of 350 people, 97 of whom have blue eyes, what is the probability that neither person has blue eyes?

Accepted Answer

$$\frac{253}{350} 	imes \frac{252}{349} = 0.522$$

Question 10

Four unrelated people in the US are selected at random. If the probability that a person has type O+ blood is 40%, what is the probability that none of the four have type O+ blood?

Accepted Answer

$$(1-0.40)^4$$ = $$0.6^4 = 0.130$

Question 11

A card is selected at random from a standard deck. What is the probability of selecting a heart and a face card (Jack, Queen, or King)?

Accepted Answer

$$\frac{3}{52} = 0.0577$$

Question 12

From a pool of 30 qualified Starfleet Officers, how many ways can you fill the positions of Captain, First Officer, Science Officer, and Chief Security Officer (order matters)?

Accepted Answer

$$30 	imes 29 	imes 28 	imes 27 = 657,720$$

Question 13

If your starship’s replicator is programmed to make meals by combining 4 choices from among 20 food options (order does NOT matter), how many different ways can you order a meal?

Accepted Answer

$$\binom{20}{4} = \frac{20!}{4!\,16!} = 4,845$$

Question 14

Given the probability distribution for the number of class-M planets found per survey mission, how do you calculate the mean (expected value) of the distribution?

Accepted Answer

$$\mu = \sum x P(x)$$

Question 15

The probability that a Jedi trained by Obiwan Kenobi will go to the Dark Side is 0.07. If Master Kenobi trains 7 apprentices, what is the probability that exactly 2 of them will turn to the Dark Side?

Accepted Answer

$$\binom{7}{2} 	imes 0.07^2$ 	imes 0.93^5$ = 0.0716$$

Question 16

For a binomial distribution with $$n = 7$$ and $$p = 0.07$$, what is the expected number (mean) of apprentices who will turn to the Dark Side?

Accepted Answer

$$\mu = n 	imes p = 7 	imes 0.07 = 0.49$$

Question 17

In the exercise habits table, what is the probability that a randomly selected female athlete's primary routine is aerobic?

Accepted Answer

$$\frac{180}{245} = 0.735$$

Question 18

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time.

Probability and Statistics Practice Test 2 – Guided Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards