Question 1: A bag contains 3 red balls and 2 blue balls. A second bag contains 4 red balls and 1 blue ball. If one ball is drawn at random from each bag, complete the probability table for the events 'Red from Bag 1' and 'Red from Bag 2'.

Answer: {"probabilityRedBag1":0.6,"probabilityRedBag2":0.8}

Question 2: Calculate the probability that both balls drawn are red, based on the tables below.

Answer: See full answer key

Question 3: Construct a probability table for two independent events: rolling a die and flipping a coin. Label the table clearly.

Answer: See student drawing

Question 4: In a class, 60% of students like maths and 40% like science. 30% like both. Fill in the missing probabilities in the table below.

Answer: {"neither":0.6,"likeMathOnly":0.3,"likeScienceOnly":0.1}

Question 5: Using the table from Question 4, what is the probability that a randomly chosen student likes either maths or science?

Answer: See full answer key

Question 6: A survey shows that 70% of people prefer tea and 50% prefer coffee, with 20% liking both. Create a table to represent these preferences.

Answer: See student drawing

Question 7: A box contains 10 apples and 15 oranges. Two fruits are picked at random without replacement. Fill in a table showing the probabilities of selecting different combinations of fruits.

Answer: {"bothApples":0.204,"bothOranges":0.308,"oneAppleOneOrange":0.488}

Question 8: Explain why the probabilities in a probability table must add up to 1. Provide a brief example.

Answer: Probabilities in a table represent all possible outcomes; their sum must be 1 because one of the outcomes must occur. Example: tossing a coin has outcomes {Heads, Tails}, probabilities {0.5, 0.5}, sum = 1.

Question 9: Identify and correct the mistake: A probability table shows probabilities adding up to 1.2. What is wrong?

Answer: Probabilities cannot sum to more than 1. The mistake is that the total is 1.2; probabilities should be adjusted so their sum is 1.

Question 10: Given two events with probabilities P(A) = 0.4 and P(B) = 0.5, and P(A and B) = 0.2, complete the probability table for the four possible outcomes.

Answer: {"AandB":0.2,"AandNotB":0.2,"NotAandB":0.3,"NotAandNotB":0.3}

Question 11: Using the table from previous question, what is the probability that either A or B (or both) occur?

Answer: See full answer key

Question 12: Challenge: Create a table for two events where the probability of each event is 0.5, and they are mutually exclusive. Show all entries.

Answer: See student drawing