Mutually Exclusive Events
This worksheet focuses on understanding and identifying mutually exclusive events in probability, including calculations and real-world examples.
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Mutually Exclusive Events
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Mutually Exclusive Events
Two events are mutually exclusive if they cannot occur at the same time. In simpler terms, if one event happens, the other cannot. For example, when you flip a coin, the event of getting a 'head' and the event of getting a 'tail' are mutually exclusive because you cannot get both at once.
1. Which of the following pairs of events is mutually exclusive when rolling a single standard six-sided die?
Rolling an even number and rolling a number greater than 3
Rolling a prime number and rolling an odd number
Rolling an odd number and rolling an even number
Rolling a number less than 4 and rolling a prime number
2. In a deck of 52 playing cards, which of the following events are mutually exclusive?
Drawing a red card and drawing a King
Drawing a face card and drawing a Club
Drawing a Spade and drawing a Heart
Drawing an Ace and drawing a Black card
3. If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0, then events A and B are mutually exclusive.
True
False
4. Drawing a red marble and drawing a blue marble from a bag containing only red and blue marbles (without replacement) are mutually exclusive events.
True
False
5. If two events cannot happen at the same time, they are called events.
6. For mutually exclusive events A and B, the probability of A or B occurring is given by the formula P(A or B) = .
7. Consider a bag containing 5 red balls, 3 blue balls, and 2 green balls. If you draw one ball at random:
a) Are the events 'drawing a red ball' and 'drawing a blue ball' mutually exclusive? Explain why.
b) Calculate the probability of drawing a red ball OR a blue ball.
8. A student is selected at random from a class. Let event A be 'the student is a boy' and event B be 'the student has long hair'. Are events A and B always mutually exclusive? Justify your answer.
9. Analyze the Venn Diagram below. Describe the relationship between Event A and Event B.