Probability Tree Diagrams Worksheet
A Grade 10 math worksheet focusing on constructing and interpreting tree diagrams for probability problems.
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Probability Tree Diagrams Worksheet
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Read each question carefully and construct a tree diagram to represent the probabilities. Use your tree diagram to answer the questions that follow. Show all your work.
1. A bag contains 3 red marbles and 2 blue marbles. A marble is drawn at random, its color is noted, and then it is replaced. A second marble is drawn. Draw a tree diagram to represent the possible outcomes and their probabilities. Then, find the probability of drawing two red marbles.
2. A fair coin is tossed three times. Draw a tree diagram to show all possible outcomes. What is the probability of getting exactly two heads?
3. In a class, 60% of students study Math and 40% study Science. Of those who study Math, 70% pass their exam. Of those who study Science, 80% pass their exam. Complete the following to calculate the probability that a randomly chosen student studies Math AND passes their exam:
P(Math and Pass) = P(Pass | Math) × P(Math) = × =
4. A company produces light bulbs, 5% of which are defective. If two light bulbs are chosen at random, what is the probability that exactly one of them is defective?
0.0025
0.0475
0.095
0.9025
5. A card is drawn from a standard deck of 52 cards. It is not replaced. A second card is drawn. Use a tree diagram to find the probability of drawing two aces.