Question 1: A researcher is studying whether students prefer tea or coffee. Out of 100 students surveyed, 60 prefer tea. What is the probability that a randomly selected student from this group prefers tea?

Answer: The probability is 60 out of 100, which simplifies to 0.6 or 60%.

Question 2: In an experiment, the chance of randomly selecting a male student from a class of 30 students is 15. What is the probability of selecting a female student?

Answer: The probability of selecting a female student is 1 - (number of males / total students). Since 15 are males, there are 15 females. Thus, the probability is 15/30 = 0.5 or 50%.

Question 3: A bag contains 10 red balls and 20 blue balls. If one ball is drawn at random, what is the probability that it is red?

Answer: The probability is 10 red balls divided by total balls: 10/30 = 1/3 ≈ 0.33 or 33%.

Question 4: Explain what is meant by the term 'probability' in the context of psychological research.

Answer: Probability refers to the likelihood or chance that a particular event will occur in a given situation, often expressed as a fraction, decimal, or percentage.

Question 5: A researcher predicts that there is a 25% chance that a new teaching method improves student performance. How many students out of 80 would you expect to benefit from this method?

Answer: Expected number of students = 25% of 80 = 0.25 × 80 = 20 students.

Question 6: A survey indicates that 70% of participants enjoy listening to music while studying. If 50 students are surveyed, how many students are expected to enjoy music while studying?

Answer: Number of students = 70% of 50 = 0.7 × 50 = 35 students.

Question 7: Describe how you would calculate the probability of an event if you know the total number of possible outcomes and the number of successful outcomes.

Answer: Probability = Number of successful outcomes divided by total number of possible outcomes.

Question 8: Draw a simple probability tree diagram to represent the chance of flipping a coin and getting either heads or tails twice in a row. Include all possible outcomes.

Answer: A correct diagram would show a starting point with two branches: one for heads and one for tails. Each branch then splits again into two, representing the second flip, resulting in four outcomes: HH, HT, TH, TT.

Question 9: A die is rolled 100 times. What is the theoretical probability of rolling a 4 on any given roll? How many times would you expect a 4 to appear in 100 rolls?

Answer: The probability of rolling a 4 is 1/6 ≈ 0.167 or 16.7%. Expected number of 4s in 100 rolls = 1/6 × 100 ≈ 16.7, so about 17 times.

Question 10: Sketch a bar chart representing the following data: Out of 50 students, 20 prefer cats, 15 prefer dogs, and 15 prefer birds. Label the axes clearly.

Answer: The bar chart should have three bars labeled 'Cats,' 'Dogs,' and 'Birds.' The height of the 'Cats' bar should correspond to 20 students, and both 'Dogs' and 'Birds' bars should correspond to 15 students each. Axes labeled accordingly.