Question 1: Explain why a probability value of 1.2 is incorrect. What is the maximum value a probability can have?

Answer: A probability cannot exceed 1; the maximum value is 1.

Question 2: A student calculates the probability of an event as 1.05. Identify the mistake and correct it.

Answer: Probabilities cannot be greater than 1; the correct value is at most 1.

Question 3: Plot the graph of y=2x for x between 0 and 1. What is the value of y when x=0.5?

Answer: 1

Question 4: A common misconception is that a probability of 0.5 means an event is equally likely to happen or not. Explain why this is a misunderstanding.

Answer: While 0.5 indicates equal likelihood in a symmetric scenario, it does not guarantee equal outcomes in all contexts; it is just a measure of likelihood.

Question 5: Identify the error: A teacher states that the probability of rain tomorrow is 1, meaning it will definitely rain. Is this correct? Why or why not?

Answer: Yes, a probability of 1 means the event will definitely occur.

Question 6: A survey reports that the probability of selecting a vegetarian is 0.4. What is the probability of not selecting a vegetarian?

Answer: 0.6

Question 7: A student claims that the probability of an event must be either 0 or 1. Is this true? Explain your answer.

Answer: No, probabilities can take any value between 0 and 1, inclusive.

Question 8: A game has a 0.75 chance of winning. What is the probability of losing? Show your calculations.

Answer: 0.25

Question 9: In a biased coin, the probability of getting heads is 0.6. A student claims that because 0.6 is close to 0.5, the coin is almost fair. Critique this statement.

Answer: Close to 0.5 suggests near-equal chances, but 'almost fair' depends on context; 0.6 indicates bias.

Question 10: Identify and correct the misconception: If the probability of event A is 0.8, then event A is almost certain, so its complement must be very unlikely.

Answer: Correct. The complement has a probability of 0.2, which is relatively low, so event A is quite likely.

Question 11: A student attempts to calculate the probability of multiple independent events occurring together by multiplying their probabilities: 0.9 and 0.8. Is this correct? Explain.

Answer: Yes, for independent events, joint probability is the product of individual probabilities: 0.72.