Question 1: Construct a 2x2 table to represent the sample space for flipping a coin twice. Fill in the cells with the possible outcomes.

Answer: HH, HT, TH, TT

Question 2: If the probability of rain is 0.3 and the probability of sun is 0.7, and assuming independence, complete a table showing the joint probabilities for 'Rain' and 'Sun' with two events: 'Rain' and 'No Rain'.

Answer: P(Rain & Rain)=0.09, P(Rain & No Rain)=0.21, P(No Rain & Rain)=0.21, P(No Rain & No Rain)=0.49

Question 3: A survey shows 60% like tea, 50% like coffee, and 30% like both. Fill in the table to represent the data, and find the probability that a person likes either tea or coffee.

Answer: P(T or C)=0.8

Question 4: Identify and correct the mistake in the following table representing two events: | Event A | Event B | Probability | |---------|---------|--------------| | Yes | Yes | 0.2 | | Yes | No | 0.3 | | No | Yes | 0.4 | | No | No | 0.2 |

Answer: Total probability sums to 1.0, but the values sum to 1.1, so one probability is incorrect.

Question 5: Using the table: | | Success | Failure | |------|---------|---------| | Group 1 | 12 | 8 | | Group 2 | 15 | 5 | Calculate the probability that a randomly selected individual from Group 1 experienced success.

Answer: 12/20 = 0.6

Question 6: In a table showing outcomes for two events, the cell for Event A = Yes and Event B = No has a probability of 0.15. If the total probability for Event A = Yes is 0.4, what is the probability that Event B = Yes given Event A = Yes?

Answer: 0.25

Question 7: Construct a table to show all outcomes when rolling two six-sided dice. Fill in the number of occurrences for each sum from 2 to 12.

Answer: Sum counts: 2(1), 3(2), 4(3), 5(4), 6(5), 7(6), 8(5), 9(4), 10(3), 11(2), 12(1)

Question 8: A box contains 3 red, 2 blue, and 5 green balls. Two balls are drawn at random without replacement. Complete the table showing the probability of drawing two balls of the same colour.

Answer: Red=3/10*2/9=1/15, Blue=2/10*1/9=1/45, Green=5/10*4/9=2/9; total same colour=1/15+1/45+2/9

Question 9: A survey finds 40% of students prefer Maths, 30% prefer Science, and 15% prefer both. Use the table to find the probability that a student prefers Maths only.

Answer: 0.25

Question 10: A factory produces two types of products, A and B, with probabilities 0.6 and 0.4 respectively. The defect rates are 2% for A and 5% for B. Construct a table to find the overall probability of a defective product.

Answer: P(defective)=0.6*0.02+0.4*0.05=0.012+0.02=0.032