Probability Tree Diagrams Worksheet

Probability Tree Diagrams

Read each question carefully and follow the instructions to construct tree diagrams and calculate probabilities.

1. A bag contains 3 red marbles and 2 blue marbles. A marble is drawn, its color is noted, and then it is replaced. A second marble is drawn. Draw a tree diagram to represent all possible outcomes.

2. In a game, a coin is flipped. If it lands on heads, you draw a card from a deck of 4 cards (Ace, King, Queen, Jack). If it lands on tails, you roll a standard six-sided die. Draw a tree diagram to show all possible outcomes.

Consider the following tree diagram for two consecutive events, A and B, where P(A) = 0.6, P(not A) = 0.4, P(B|A) = 0.7, P(not B|A) = 0.3, P(B|not A) = 0.2, and P(not B|not A) = 0.8.

3. What is the probability of event A and event B occurring, P(A and B)?

4. What is the probability of event B occurring, P(B)?

5. A student takes two tests. The probability of passing the first test is 0.7. If the student passes the first test, the probability of passing the second test is 0.8. If the student fails the first test, the probability of passing the second test is 0.4. Draw a tree diagram and use it to find the probability that the student passes exactly one test.

6. Using the information from question 5, if the student passed the second test, the probability that they also passed the first test is approximately  .