Question 1: A bag contains 3 red and 2 blue balls. Two balls are drawn at random without replacement. Complete the probability table for the possible outcomes of colour combinations and calculate the probability of drawing two red balls.

Answer: 0.3

Question 2: Construct a table showing the probabilities of selecting a student who passes or fails an exam, given that 60% pass and 40% fail. Assume the probability of passing and failing independently with two different subjects.

Answer: {"fail_subject1":0.4,"fail_subject2":0.4,"pass_subject1":0.6,"pass_subject2":0.6}

Question 3: In a survey, 40% of people like tea, 30% like coffee, and 10% like both. Fill in the table for the probabilities of liking tea only, coffee only, both, and neither.

Answer: {"both":0.1,"neither":0.4,"tea_only":0.3,"coffee_only":0.2}

Question 4: Calculate the joint probability of a student failing Maths but passing Science, given that 70% pass Science and 60% pass Maths, with 50% passing both.

Answer: 0.3

Question 5: A survey shows 55% of people prefer cats, 45% prefer dogs, and 20% prefer both. Complete the probability table and find the probability that a person prefers only cats.

Answer: 0.35

Question 6: A box contains 4 defective and 6 non-defective items. Two items are selected at random without replacement. Fill in the probability table for defective and non-defective outcomes, and find the probability that both are non-defective.

Answer: 0.36

Question 7: Construct a table showing the probabilities of selecting a card that is red or black from a standard deck, and then determine the probability of drawing a red card given that the card is even-numbered.

Answer: 0.25

Question 8: A model predicts that the probability of rain is 0.3 and the probability of snow is 0.2, with a 0.1 chance of both. Fill in the probability table and find the probability of neither rain nor snow.

Answer: 0.6

Question 9: A factory produces widget A and B. 70% of widgets A pass quality control, 80% of B pass, and 60% pass both. Fill in the table for outcomes and determine the probability that a widget passes neither quality control check.

Answer: 0.12

Question 10: Identify and correct the mistake in the following probability table where the total probability sums to 1.2, not 1: | Outcomes | Probability | |----------|--------------| | Both | 0.3 | | Only A | 0.4 | | Only B | 0.3 | | Neither | 0.2 |

Answer: The total sum is 1.2; probabilities must sum to 1. The mistake is the sum of probabilities being too high. Adjust values so total equals 1.