Question 1: A researcher is studying the likelihood of students passing a psychology test. Out of 100 students, 60 passed. What is the probability that a randomly selected student passed the test? Express your answer as a fraction, decimal, and percentage.

Answer: Fraction: 60/100 or 3/5; Decimal: 0.6; Percentage: 60%

Question 2: If the probability of a participant experiencing a certain side effect during a study is 1 in 20, what is the probability that a participant will NOT experience this side effect?

Answer: The probability of not experiencing the side effect is 19/20 or 0.95 or 95%.

Question 3: A bag contains 5 red balls and 15 blue balls. If a ball is randomly drawn, what is the probability it is red? What is the probability it is blue?

Answer: Red: 5/20 or 1/4; Blue: 15/20 or 3/4

Question 4: Explain why understanding probability is important when designing psychological experiments.

Answer: Understanding probability helps researchers determine the likelihood that results occurred by chance, ensuring findings are valid and not due to random variation.

Question 5: A survey shows that 30% of people prefer a certain therapy. If 10 people are randomly selected, what is the probability that exactly 3 prefer this therapy? (Use the binomial probability formula or approximation)

Answer: The probability is given by the binomial formula: P = C(10,3) × (0.3)^3 × (0.7)^7, which calculates to approximately 0.266 (26.6%).

Question 6: Describe a situation in psychological research where the probability of an event might be used to interpret results.

Answer: When testing if a new teaching method improves memory, researchers might calculate the probability that observed improvements occurred by chance, to determine if the method is effective.

Question 7: Sketch a simple diagram illustrating the concept of probability distribution for a six-sided die roll. Label the axes and the probabilities for each outcome.

Answer: A bar graph with the x-axis labeled 'Die Face (1-6)' and the y-axis labeled 'Probability'. Each bar should be equal height at 1/6, showing uniform distribution.

Question 8: In an experiment, the probability of a participant correctly recalling information is 0.8. What is the probability that in a group of 5 participants, exactly 4 will recall correctly? (Use the binomial formula or approximation).

Answer: Using the binomial formula: P = C(5,4) × (0.8)^4 × (0.2)^1 ≈ 0.4096.

Question 9: A psychologist claims that the probability of a certain event is 0.05. What does this imply about the likelihood of the event happening in a large number of trials?

Answer: It implies that the event is unlikely to occur in any single trial, but given many trials, it could still happen occasionally, approximately 5% of the time.

Question 10: Create a brief scenario where understanding probability would help a psychologist decide whether a treatment's success rate is significant or due to chance. Include the key figures and reasoning.

Answer: A psychologist tests a new therapy on 50 patients, with 35 showing improvement. The baseline success rate is 50%. The psychologist calculates the probability of 35 or more successes occurring by chance if the true success rate is 50%. If this probability is very low (e.g., less than 5%), it suggests the treatment is effective beyond chance.