Question 1: A psychologist conducts a study with 200 participants, of which 60 are male. What is the probability that a randomly selected participant is male?

Answer: The probability is 60 divided by 200, which simplifies to 0.3 or 30%.

Question 2: In a class of 30 students, 18 prefer chocolate ice cream, and the rest prefer vanilla. If a student is chosen at random, what is the probability they prefer vanilla?

Answer: Total students = 30; students who prefer vanilla = 30 - 18 = 12; probability = 12/30 = 0.4 or 40%.

Question 3: Explain what is meant by 'probability' in the context of psychological research.

Answer: Probability in psychological research refers to the likelihood or chance that a particular event or outcome will occur, often expressed as a number between 0 and 1 or as a percentage.

Question 4: A researcher wants to determine the probability of a participant having a specific trait based on past data. If 40 out of 100 previous participants had this trait, what is the probability for a new participant?

Answer: The probability is 40/100, which simplifies to 0.4 or 40%.

Question 5: Describe a scenario in psychological research where understanding probability is essential.

Answer: In determining whether the results of an experiment are statistically significant, researchers calculate the probability that the observed effects occurred by chance.

Question 6: A survey shows that 25% of people in a city prefer a new mental health app. If 8 people are randomly selected, what is the probability that exactly 2 of them prefer the app? (Use the binomial probability formula.)

Answer: Using the binomial formula: P = (n choose k) * p^k * (1-p)^(n-k). Here, n=8, k=2, p=0.25. So, P = (8 choose 2) * 0.25^2 * 0.75^6. Calculate accordingly.

Question 7: Draw a tree diagram to represent the probability of flipping a coin twice and getting at least one head. Label all branches clearly.

Answer: A correct tree diagram would have the first flip with branches for Heads and Tails, and each branch leading to the second flip with similar branches. The paths leading to at least one head include: Heads-Heads, Heads-Tails, Tails-Heads.

Question 8: Sketch a simple diagram to illustrate the concept of independent events in probability. Use two events, A and B, and demonstrate their relationship.

Answer: A Venn diagram with two circles that do not overlap, labeled A and B, representing two independent events with no intersection.

Question 9: A psychologist is studying the probability of a certain response occurring after a stimulus. If previous data shows a 0.2 probability of response per trial, what is the probability of observing the response in 3 consecutive trials?

Answer: The probability of response in 3 consecutive trials (assuming independence) is 0.2 * 0.2 * 0.2 = 0.008 or 0.8%.

Question 10: Explain why understanding probability is important when interpreting the results of psychological experiments.

Answer: Understanding probability helps psychologists determine whether their results are due to chance or represent a true effect, thus informing the validity of their conclusions.