Question 1: A bag contains 3 red and 2 blue balls. Two balls are drawn at random without replacement. Construct a grid to show all possible outcomes of the colors of the two balls drawn. Label the rows as the color of the first ball and the columns as the color of the second ball.

Answer:

Question 2: Using your grid from Question 1, calculate the probability that both balls drawn are red.

Answer: 1/3

Question 3: A survey shows that 60% of students prefer tea and 40% prefer coffee. Some students prefer both. Construct a grid to represent the survey data, with one axis for tea and the other for coffee. Complete the grid with the counts if there are 50 students in total.

Answer:

Question 4: If 12 students prefer both tea and coffee, how many students prefer only tea? Show your working.

Answer: 18

Question 5: A factory produces two types of light bulbs—incandescent and LED. The probability of selecting an incandescent bulb is 0.6, and an LED bulb is 0.4. A quality check shows that 10% of incandescent bulbs are defective, and 5% of LED bulbs are defective. Construct a grid to show the distribution of bulbs by type and defectiveness.

Answer:

Question 6: Using the grid from Question 5, find the probability that a randomly chosen bulb is either defective or LED.

Answer: 0.215

Question 7: A school offers two extracurricular activities: Drama and Sports. 70% of students participate in Drama, 50% in Sports, and 30% participate in both. Draw a grid to represent this data and calculate the percentage of students who do not participate in either activity.

Answer: 30%

Question 8: A researcher studies two independent traits: Eye Color (Brown or Blue) and Hair Color (Black or Blonde). The probability of having brown eyes is 0.6, and black hair is 0.7. Construct a grid showing the distribution of traits assuming independence. Calculate the probability that a person has blue eyes and blonde hair.

Answer: 0.12

Question 9: In a certain town, 80% of households own a car, and 65% own a bicycle. If 50% own both, construct a grid to represent this data. What percentage of households own neither a car nor a bicycle?

Answer: 15%

Question 10: A box contains 4 defective and 6 non-defective items. Two items are drawn at random without replacement. Draw a grid to show all possible outcomes and determine the probability that the first item is defective and the second item is non-defective.

Answer: 8/45

Question 11: Identify and correct the mistake in the following grid representation of a sample space where students choose a snack (Chips or Fruit) and a drink (Soda or Water), but the total probabilities do not sum to 1.

Answer: Students should ensure probabilities in all cells sum to 1; common mistake is double-counting or incorrect probabilities assigned.

Question 12: Challenge: A survey shows that 55% of people like tea only, 25% like coffee only, 10% like both, and the rest dislike both. Represent this data in a grid, and find the percentage of people who dislike both drinks.

Answer: 10%