Q: A box contains 4 defective and 16 non-defective bulbs. If two bulbs are drawn one after another without replacement, what is the probability that both are defective?

$$\frac{4}{20} \times \frac{3}{19}$$

Question 1

A password consists of 3 letters followed by 2 digits. If letters and digits can be repeated, how many different passwords are possible?

Accepted Answer

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

Question 2

A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is not blue?

Accepted Answer

$$\frac{7}{10}$$

Question 3

Given the following probability distribution for a discrete random variable $$X$$:

$$\begin{align*}
X & : 0 & 1 & 2 \
P(X) & : 0.2 & 0.5 & 0.3 \
\end{align*}$$

What is the mean $$\mu of$$ $$X$$?

Accepted Answer

$$1.1$$

Question 4

A standard deck of 52 cards is shuffled. What is the probability that a card drawn at random is a heart or a face card (Jack, Queen, King)?

Accepted Answer

$$\frac{22}{52}$$

Question 5

A medical test for a disease is 95% accurate. If 2 people are tested independently, what is the probability that both tests are accurate?

Accepted Answer

$$0.95 	imes 0.95 = 0.9025$$

Question 6

A committee of 4 is to be chosen from 7 men and 5 women. How many different committees can be formed?

Accepted Answer

$$\binom{12}{4}$$

Question 7

Which of the following is a continuous random variable?

Accepted Answer

The time (in minutes) it takes to run a marathon

Question 8

A box contains 4 defective and 16 non-defective bulbs. If two bulbs are drawn one after another without replacement, what is the probability that both are defective?

Accepted Answer

$$\frac{4}{20} 	imes \frac{3}{19}$$

Question 9

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.4 + 0.5 - 0.2 = 0.7$$

Question 10

A fair coin is tossed 8 times. What is the probability of getting exactly 3 heads?

Accepted Answer

$$\binom{8}{3} (0.5)^3$ (0.5)^5$

Question 11

A discrete probability distribution has $$\mu = 2$$ and $$\$$sigma^2$$ = 1.5. $$What is the standard deviation $$\sigma$$?

Accepted Answer

$$\sqrt{1.5}$$

Question 12

A student must answer 5 out of 10 questions on an exam. In how many ways can the student choose the questions?

Accepted Answer

$$\binom{10}{5}$$

Question 13

If $$P(A) = 0.7$$, what is the probability that event $$A$$ does not happen?

Accepted Answer

$$1 - 0.7 = 0.3$$

Question 14

A binomial experiment has $$n = 12$$ trials and probability of success $$p = 0.3. $$What is the mean $$\mu of $$the distribution?

Accepted Answer

$$12 	imes 0.3 = 3.6$$

Question 15

A survey found that 60% of people prefer coffee, 50% prefer tea, and 30% like both. What is the probability that a randomly selected person likes coffee or tea?

Accepted Answer

$$0.6 + 0.5 - 0.3 = 0.8$$

Question 16

A company has 8 managers and wants to assign a president and a vice president. How many ways can these positions be filled?

Accepted Answer

$$8 	imes 7 = 56$$

Question 17

A box contains 3 red and 7 blue balls. If two balls are drawn at random with replacement, what is the probability both are red?

Accepted Answer

$$\left(\frac{3}{10}\$$right)^2$$ = \frac{9}{100}$$

Question 18

Which formula would you use to find the probability of getting exactly $$k$$ successes in $$n$$ independent Bernoulli trials with probability $$p of $$success?

Accepted Answer

$$P(k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 19

A table shows that 40 students take math, 30 take science, and 10 take both. If a student is chosen at random, what is the probability the student takes math given they take science?

Accepted Answer

$$\frac{10}{30} = \frac{1}{3}$$

Question 20

Which of the following is NOT a property of a probability distribution for a discrete random variable?

Accepted Answer

The sum of all probabilities is greater than 1

Probability and Discrete Probability Distributions: Exam 2 Study Guide

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