Question 1: Construct a 4x3 grid to represent all possible outcomes when flipping a coin twice and rolling a 3-sided die.

Answer: Outcome cells total 12, with 4 rows for coin outcomes and 3 columns for die outcomes.

Question 2: If 2 outcomes are shaded in a 5x5 grid, what is the probability of randomly selecting a shaded outcome?

Answer: 0.08

Question 3: List all outcomes in a 2x2 grid where the first event (A) is selecting a red object and the second event (B) is choosing an even number.

Answer: Red & 2, Red & 4, Not Red & 2, Not Red & 4

Question 4: Calculate the probability that neither event occurs if the total grid size is 16 and 4 outcomes involve event A happening, 5 involve event B, with 2 outcomes overlapping.

Answer: Probability = 1 - (P(A) + P(B) - P(A and B)) = 1 - (4/16 + 5/16 - 2/16) = 1 - (7/16) = 9/16

Question 1: A 6x6 grid represents all possible outcomes when choosing a fruit (apple, banana, cherry) and a drink (juice, soda, water). How many outcomes are there, and what fraction of the grid represents choosing a cherry or a soda?

Answer: 36 outcomes; cherry or soda = (cherry=6 outcomes) + (soda=6 outcomes) - (cherry & soda=1 outcome) = 11/36

Question 2: Construct a grid to model selecting a day (Weekday/Weekend) and a weather condition (Rainy/Sunny). Then, shade all outcomes where it is a weekend and sunny. How many outcomes are shaded?

Answer: Weekend & Sunny = 2 outcomes

Question 3: If you randomly select from a 4x4 grid, what is the probability of selecting an outcome where both events occur if 6 outcomes fit both conditions?

Answer: 6/16 = 3/8

Question 4: Explain why shading fewer outcomes on a grid increases the probability of a specific event. Support your answer with an example.

Answer: Shading fewer outcomes reduces the total possible outcomes, increasing the likelihood of selecting a desired outcome.

Question 1: A school survey records student preferences for sports and music classes using a 3x3 grid. If 4 students prefer both sports and music, and 6 prefer sports only, how many students are surveyed if 9 outcomes are represented?

Answer: Total students = 6 (sports only) + 4 (both) + others; since total outcomes are 9, and 6+4=10, which exceeds total, rechecking: 6 sports only + 4 both = 10, so total surveyed is 10 students.

Question 2: Design a grid to represent a scenario where a person chooses a mode of transport (Car, Bus, Bike) and a time of day (Morning, Afternoon, Evening). How many possible choices are there?

Answer: 3 modes x 3 times = 9 outcomes.

Question 1: Create a 5x5 grid to model selecting a letter from A, B, C, D, E and a number from 1 to 5. Shade outcomes where the letter is either A or B, and the number is greater than 3. How many outcomes are shaded?

Answer: A or B = 2 letters; numbers >3 = 4 outcomes each; total shaded = 2 x 2 x 4 = 16 outcomes.

Question 2: Given a 4x4 grid representing two events, if 5 outcomes are shaded in the top-left quadrant and 3 in the bottom-right, what is the probability that a randomly selected outcome is in either of these shaded areas?

Answer: Total shaded outcomes = 5 + 3 = 8; probability = 8/16 = 1/2.

Question 3: Identify a common mistake when shading outcomes in a grid for two events and suggest how to avoid it.

Answer: Common mistake: double-counting overlapping outcomes. Avoid by clearly marking and counting each shaded area separately, then adjusting for overlaps.