Q: A shipment of 5000 batteries has a 5% defect rate. What is the expected number of defective batteries and the standard deviation?

Expected: $$250$$, SD: $$\sqrt{5000 \times 0.05 \times 0.95}$$

Q: If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A \cap B) = 0.12$$, are $$A$$ and $$B$$ independent?

Yes, because $$0.3 \times 0.4 = 0.12$$

Q: Suppose you draw two cards in succession without replacement from a standard deck. What is the probability that both cards are black?

$$\frac{26}{52} \times \frac{25}{51}$$

Question 1

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

The mean must be greater than the variance.

Question 2

In a binomial experiment with $$n$$ trials and probability of success $$p$$, what does the random variable $$X$$ represent?

Accepted Answer

The number of successes in $$n$$ trials.

Question 3

If events $$A$$ and $$B$$ are independent, which formula correctly gives $$P(A \cap B)$$?

Accepted Answer

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

Question 4

A shipment of 5000 batteries has a 5% defect rate. What is the expected number of defective batteries and the standard deviation?

Accepted Answer

Expected: $$250$$, SD: $$\sqrt{5000 	imes 0.05 	imes 0.95}$$

Question 5

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

Accepted Answer

$$0.9$$

Question 6

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

Accepted Answer

$$\frac{19}{52}$$

Question 7

Which of the following statements about the mean and variance of a binomial distribution is correct?

Accepted Answer

Mean: $$np$$, Variance: $$npq$$

Question 8

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A \cap B) = 0.12$$, are $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because $$0.3 	imes 0.4 = 0.12$$

Question 9

A fair die is rolled. What is the probability of getting an odd number or a number greater than 4?

Accepted Answer

$$\frac{2}{3}$$

Question 10

Suppose you draw two cards in succession without replacement from a standard deck. What is the probability that both cards are black?

Accepted Answer

$$\frac{26}{52} 	imes \frac{25}{51}$$

Question 11

Which of the following best describes the expected value of a discrete random variable $$X$$?

Accepted Answer

The long-run average value of $$X$$ over many repetitions.

Question 12

If $$P(E) = 0.3$$, what are the odds in favor of $$E$$?

Accepted Answer

$$3:7$$

Question 13

A binomial experiment consists of 10 trials with $$p = 0.2. $$What is the probability of exactly 2 successes?

Accepted Answer

$$\binom{10}{2} (0.2)^2$ (0.8)^8$

Question 14

Which of the following is TRUE about the variance of a discrete probability distribution?

Accepted Answer

Variance measures the spread of the distribution.

Question 15

If $$A$$ and $$B$$ are not mutually exclusive, which formula gives $$P(A \cup B)$$?

Accepted Answer

$$P(A) + P(B) - P(A \cap B)$$

Question 16

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is $$E(X)$$?

Accepted Answer

$$2.1$$

Question 17

A student claims that the expected value of a random variable can never be negative. Is this statement true or false?

Accepted Answer

False, because the expected value can be negative if the values of the random variable are negative.

Question 18

A quality control procedure randomly selects 30 batteries from a shipment and accepts the shipment if there are less than three defective batteries in the sample. If the defect rate is 5%, what is the probability that the shipment is accepted?

Accepted Answer

$$P(X \u003c 3)$$ where $$X \sim Binomial(n=30, p=0.05)$$

Question 19

Which of the following best describes the mean of a random variable of a probability distribution?

Accepted Answer

It is the weighted average of all possible values.

Question 20

A five-digit code is created where the first digit must be odd and the second digit cannot be zero. Digits may repeat. How many such codes are possible?

Accepted Answer

$$5 	imes 9 	imes 10 	imes 10 	imes 10$$

Probability and Discrete Probability Distributions: Study Notes and Practice Questions

Study Guide - Practice Questions

Study Guide - Flashcards