Non-Disjoint Events Probability Worksheet

Non-Disjoint Events Probability

Read each question carefully and calculate the probabilities for non-disjoint events. Show all your work.

1. Which of the following pairs of events are non-disjoint (overlapping) when drawing a single card from a standard deck of 52 cards?

2. If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, what is P(A or B)?

3. The Addition Rule for non-disjoint events states that P(A or B) = P(A) + P(B) - P(  and  ).

4. If two events have at least one outcome in common, they are considered   events.

5. A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning an even number or a number greater than 5? Show your work.

6. In a class of 30 students, 15 students play basketball, 10 students play soccer, and 5 students play both. What is the probability that a randomly chosen student plays basketball or soccer? Show your work.

7. Use the Venn Diagram below to answer the following questions:

a) What are the elements in set A?

b) What are the elements in set B?

c) What are the elements in A and B (A ∩ B)?

d) What are the elements in A or B (A U B)?

8. The probability of two non-disjoint events occurring is always less than the probability of either event occurring individually.

9. If events A and B are disjoint, then P(A or B) = P(A) + P(B).