Question 1: Construct a 4x4 grid to represent all possible outcomes when flipping a coin twice. Shade the outcomes where both flips are heads.

Answer: Correctly shaded top-left 2x2 cells

Question 2: Calculate the probability of getting exactly one head when flipping three coins. Show your grid and working.

Answer: 3/8

Question 3: In a 5x5 grid representing two events, identify and correct the common mistake made when shading outcomes where event A occurs but event B does not.

Answer: Incorrect shading; students should shade all cells in the row/column for event A only

Question 1: A spinner is divided into 6 equal parts labeled 1 to 6. Students draw a 6x6 grid to show all possible outcomes when spinning twice. If a student claims that outcomes with the same number on both spins are impossible to shade, identify the mistake and correct it.

Answer: Mistake: They ignored outcomes like (1,1), (2,2), etc. The correction is to shade the diagonal cells where both spins are the same.

Question 2: Using a 4x4 grid, explain how to determine the probability of both events A and B occurring, given A is shaded in the first row and B in the first column. Describe how overlapping shading affects the calculation.

Answer: Overlapping shaded cells indicate outcomes where both A and B occur; count these cells and divide by total outcomes.

Question 1: A school has 3 different clubs (Drama, Science, Art). Students can join one or more clubs. Construct a grid to show all possible combinations of club memberships, then shade outcomes where a student joins Drama and Art but not Science. Identify and explain any common shading mistake students might make.

Answer: Correct shading includes the cells where Drama and Art are joined but Science is not; common mistake is shading cells where Science is also joined.

Question 1: Construct a 6x6 grid to represent two independent events, each with 6 outcomes. A student claims that outcomes where the same number appears in both events are impossible to shade, but this is incorrect. Identify the mistake and shade these outcomes correctly.

Answer: Mistake: They think matching outcomes are impossible. Correct shading involves marking the diagonal cells where outcomes are the same.

Question 2: Given two events with probabilities 1/3 and 1/4 respectively, draw the corresponding grid and explain how the overlap affects the calculation of the probability of both events occurring.

Answer: Overlap must be counted to find joint probability; grid helps visualize the combined outcomes.

Question 1: Draw and shade a 3x3 grid representing two events, where event A occurs in the first row and event B in the first column. Shade outcomes where either A or B occurs, but not both.

Answer: Cells in the first row and first column excluding the diagonal

Question 2: A student incorrectly shades only the outcomes where event A occurs, ignoring overlaps. Explain why this is a misconception and how to properly shade outcomes for two events.

Answer: Incorrect shading misses outcomes where both A and B occur; proper shading includes all outcomes where A, B, or both occur.