Q: Given $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \text{ and } B) = 0.2$$, what is $$P(A \text{ or } B)$$?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = 0.7$$

Q: If events A and B are independent, and $$P(A) = 0.3$$, $$P(B) = 0.6$$, what is $$P(A \text{ and } B)$$?

$$P(A \text{ and } B) = P(A) \times P(B) = 0.18$$

Q: A medical test for a disease has sensitivity of 90% and specificity of 80%. If the prevalence of the disease is 5%, what is the probability that a randomly selected person tests positive?

$$0.05 \times 0.90 + 0.95 \times 0.20 = 0.265$$

Q: In a tree diagram for flipping two coins, what is the probability of getting at least one heads?

$$1 - P(\text{no heads}) = 1 - 0.25 = 0.75$$

Question 1

Which of the following best describes a random experiment?

Accepted Answer

An experiment where the outcome cannot be predicted with certainty, even if all conditions are known.

Question 2

A bag contains 3 red, 2 blue, and 5 green marbles. If you draw one marble at random, how many different ways can the experiment end?

Accepted Answer

3

Question 3

Which of the following statements correctly differentiates empirical probability from theoretical probability?

Accepted Answer

Empirical probability is based on observed data from experiments, while theoretical probability is calculated using known formulas and assumptions.

Question 4

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

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B) = 0.7$$

Question 5

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Drawing a red card and drawing a black card from a standard deck.

Question 6

If events A and B are independent, and $$P(A) = 0.3$$, $$P(B) = 0.6$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B) = 0.18$$

Question 7

A medical test for a disease has sensitivity of 90% and specificity of 80%. If the prevalence of the disease is 5%, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.05 	imes 0.90 + 0.95 	imes 0.20 = 0.265$$

Question 8

In a study, 100 smokers and 100 non-smokers are followed for 10 years. 20 smokers develop lung cancer, while 5 non-smokers do. What is the relative risk of lung cancer for smokers compared to non-smokers?

Accepted Answer

$$\frac{20/100}{5/100} = 4$$

Question 9

Which of the following best describes a parameter in statistics?

Accepted Answer

A value that describes a characteristic of a population.

Question 10

Which sampling method is most appropriate for ensuring that all subgroups of a population are represented proportionally?

Accepted Answer

Stratified random sampling

Question 11

A survey is sent to 1000 people, but only 200 respond. Which type of bias is most likely present?

Accepted Answer

Non-response bias

Question 12

A frequency histogram of exam scores shows a long tail to the right. What is the shape of the distribution?

Accepted Answer

Right-skewed

Question 13

Given the sample data: 2, 4, 6, 8, 10. What is the sample mean?

Accepted Answer

$$\frac{2+4+6+8+10}{5} = 6$$

Question 14

For the data set: 1, 3, 5, 7, 9, what is the sample median?

Accepted Answer

5

Question 15

Given the data: 10, 12, 14, 16, 18, what is the interquartile range (IQR)?

Accepted Answer

IQR = Q3 - Q1 = 16 - 12 = 4

Question 16

If a sample has mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, what is the z-value for a score of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 17

According to the 68-95-99% Rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 18

A researcher wants to study the effect of a new drug. She randomly assigns participants to either the drug or a placebo group, and neither the participants nor the researchers know who receives which treatment. What type of study is this?

Accepted Answer

Double-blinded experimental study

Question 19

In a tree diagram for flipping two coins, what is the probability of getting at least one heads?

Accepted Answer

$$1 - P(	ext{no heads}) = 1 - 0.25 = 0.75$$

STAT 205 Midterm 1 Study Guide: Probability, Data Collection, and Descriptive Statistics

Study Guide - Practice Questions

Study Guide - Flashcards