Question 1: Construct a tree diagram representing three independent events: flipping a coin twice and rolling a six-sided die once. Label all branches clearly.

Answer:

Question 2: Calculate the probability of getting exactly one Heads in two coin flips and rolling a 4 on the die.

Answer: 0.125

Question 3: If the probability of rain is 0.3 and the probability of snow is 0.2 independently, draw a tree diagram for the weather over two days, considering rain, snow, or clear days.

Answer:

Question 4: Using your diagram, find the probability that both days are rainy.

Answer: 0.09

Question 1: A student randomly selects a card from a deck, then flips a coin. Using a tree diagram, find the probability that the student picks a spade and then gets heads. Explain each step.

Answer:

Question 2: In a game, a spinner with four equal sections and a die are spun/rolled independently. Construct the tree diagram and determine the probability of spinning a number greater than 2 and rolling an even number.

Answer:

Question 3: Identify and explain the mistake in the following probability calculation based on a tree diagram: 'Probability of A or B = P(A) + P(B) - P(A and B)', when events are assumed independent but are actually mutually exclusive.

Answer:

Question 1: A factory produces three types of products: A, B, and C. The chance of defect in each product is 0.05, 0.02, and 0.01 respectively. Construct a tree diagram to represent selecting a product and checking for defects. Calculate the probability of selecting a product and finding no defect.

Answer:

Question 2: A school surveys students' preferences for sports: soccer (60%), basketball (25%), volleyball (15%). Construct a tree diagram for choosing a sport over two days, assuming preferences are independent day-to-day. Find the probability that a student prefers soccer both days.

Answer: 0.36

Question 1: Design a tree diagram for a scenario where a student answers 3 multiple-choice questions, each with 4 options, and all choices are independent. Calculate the probability that the student answers all questions correctly if the chance of choosing the correct answer for each is ¼.

Answer:

Question 2: Suppose in a lottery, three independent events determine the final prize: winning ticket, random draw, and bonus round. Each has a 50% chance. Construct the tree diagram and find the probability of winning a prize in at least two of the three events.

Answer:

Question 1: A student constructs a tree diagram for two independent events, but mistakenly multiplies probabilities from different branches to find the combined probability. Identify and explain the mistake.

Answer:

Question 2: A tree diagram shows the probability of selecting a red or blue ball, then drawing a yellow ball afterward. The student incorrectly adds probabilities instead of multiplying. Explain why this is wrong and how to correct it.

Answer:

Question 3: In a complex tree diagram, a student forgets to include certain branches, leading to probabilities summing to more than 1. Identify the error and describe how to ensure the tree diagram is complete.

Answer: