Understanding Non-Disjoint Events
Explore non-disjoint events in probability with this Grade 6 math worksheet, featuring exercises on Venn diagrams and calculating probabilities.
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Understanding Non-Disjoint Events
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Read each question carefully and answer to the best of your ability. Show your work where applicable.
Non-disjoint events are events that can happen at the same time. The overlap between these events needs to be considered when calculating probabilities.
Consider two events, A and B. If A and B are non-disjoint, it means there are outcomes that are in BOTH A and B. The probability of A or B occurring is P(A or B) = P(A) + P(B) - P(A and B).
1. If two events are non-disjoint, they cannot happen at the same time.
True
False
2. The probability of two non-disjoint events A and B occurring is found by adding P(A) and P(B) without subtracting anything.
True
False
3. Which of the following pairs of events are non-disjoint?
Rolling an even number and rolling an odd number on a six-sided die.
Drawing a red card and drawing a black card from a deck of cards.
Drawing a Queen and drawing a red card from a deck of cards.
Flipping a head and flipping a tail on a coin.
4. If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, what is P(A or B)?
0.9
0.7
1.1
0.3
Venn diagrams are useful for visualizing relationships between sets and understanding non-disjoint events.
5. In a Venn diagram, the overlapping region represents the outcomes that are in .
6. When two events are non-disjoint, we must the probability of their intersection to avoid double-counting.
7. A bag contains 10 balls: 5 red, 3 blue, and 2 green. What is the probability of drawing a red ball or a green ball? Are these events disjoint or non-disjoint? Explain your reasoning.
8. In a class of 30 students, 15 play basketball, 10 play soccer, and 5 play both. What is the probability that a randomly chosen student plays basketball or soccer?