Non-disjoint Events in Probability
Explore non-disjoint events, their properties, and how to calculate probabilities involving them using Venn diagrams and the Addition Rule.
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Non-disjoint Events in Probability
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
Two events are considered non-disjoint (or overlapping) if they can both occur at the same time. This means their intersection is not empty. The probability of A or B occurring when they are non-disjoint is given by the Addition Rule: P(A or B) = P(A) + P(B) - P(A and B).
1. Which of the following pairs of events are non-disjoint?
Drawing a red card and drawing a black card from a standard deck.
Rolling an even number and rolling an odd number on a six-sided die.
Drawing a King and drawing a Heart from a standard deck.
Flipping a head and flipping a tail on a coin.
2. A single card is drawn from a standard 52-card deck. What is the probability of drawing a Queen or a Club?
3. Use the Venn diagram below to answer the following questions.
a) P(A) =
b) P(B) =
c) P(A and B) =
d) P(A or B) =
4. If two events are non-disjoint, their intersection must be an empty set.
True
False
5. The Addition Rule for two non-disjoint events A and B is P(A or B) = P(A) + P(B) - .
6. In a class of 30 students, 17 students play basketball, 15 students play soccer, and 8 students play both. What is the probability that a randomly selected student plays basketball or soccer?