Question 1: Construct a tree diagram for two independent events: drawing a red or blue ball from a bag (probability of red 0.6), then flipping a coin where heads is 0.7. Label all branches clearly.

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Question 2: Calculate the probability of drawing a red ball and then flipping tails.

Answer: 0.6 × 0.3 = 0.18

Question 3: If the probability of selecting a green ball is 0.4, and the probability of getting heads on a coin flip is 0.5, what is the probability of not selecting green and getting tails?

Answer: 0.6 × 0.5 = 0.3

Question 4: Construct a tree diagram for three independent events: choosing a fruit (apple or banana), then a drink (juice or water), then a snack (cookie or fruit).

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Question 1: A student flips a coin three times. Construct a tree diagram showing all possible outcomes. Then, find the probability of getting exactly two heads.

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Question 2: A factory produces packets of cereal, which can be either plain or honey-flavored, and are either small or large. The probabilities are: plain 0.6, honey 0.4, small 0.7, large 0.3. Construct a tree diagram and find the probability that a randomly selected packet is honey-flavored and large.

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Question 3: Explain why the probabilities along each branch of a tree diagram for independent events multiply to give the joint probability.

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Question 4: A multiple-choice question has 3 options. The student guesses randomly and then answers a second question with 4 options, also guessing. Construct a tree diagram and determine the probability that the student guesses both questions correctly.

Answer: 1/3 × 1/4 = 1/12

Question 5: In a game, the chance of winning a round is 0.25, independently of previous rounds. If the player plays 4 rounds, construct a tree diagram and find the probability of winning exactly 2 rounds.

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Question 1: A survey shows that 70% of people prefer tea and 30% prefer coffee. If 2 people are selected at random, construct a tree diagram to represent their preferences. What is the probability both prefer tea?

Answer: 0.7 × 0.7 = 0.49

Question 2: A school has a 0.6 probability that a student passes a math test and a 0.4 probability they pass an English test independently. Construct a tree diagram and find the probability that a student passes both tests.

Answer: 0.6 × 0.4 = 0.24

Question 3: A factory produces two types of gadgets: type A and type B. The probability of a gadget being defective is 0.05 for A and 0.1 for B. If a gadget is tested and found defective, what is the probability that it is type B?

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Question 1: Construct a tree diagram for three independent events with varying probabilities: selecting a type of pet (cat with 0.5, dog with 0.5), then a type of food (kibble with 0.6, treats with 0.4), then a toy (ball with 0.3, squeaky toy with 0.7). Calculate the probability of choosing a dog, treats, and a squeaky toy.

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Question 2: A roulette wheel has 4 equally likely sectors. The wheel is spun 3 times independently. Construct a tree diagram to show all outcomes and determine the probability that exactly two reds occur if red appears in 2 sectors.

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Question 1: A student constructs a tree diagram for two independent events but multiplies probabilities along branches incorrectly. Identify and explain the mistake.

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Question 2: A common mistake is to add probabilities instead of multiplying for independent events. Provide an example where this mistake occurs and explain the correct method.

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