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Probability Distributions and Mutually Exclusive Events
When finding the probability of something, you are finding how likely it is that some event will happen.
If the probability is zero, then there is no chance of the event happening. If the probability is 1, then
there is a 100 percent chance of the event happening.
To find the probability of an event happening you have to divide the number of successful outcomes by
the number of possible outcomes.
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Sample Space – a list of all possible outcomes
Probability Distribution – a list that describes the probabilities of all possible numerical outcomes
P(A or B) means that you are finding the probability that event A or event B happens.
P(A and B) means that you are finding the probability that event A and event B both happen on the
same outcome.
Events are mutually exclusive (or disjoint) if they cannot happen at the same time.
The Addition Rule for mutually exclusive events states that if two events are mutually exclusive, then
(
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If the events are not mutually exclusive then you have to subtract the probabilities that are counted
twice (once with calculating the probability of event A and then again when calculating the probability of
)
( )
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event B). (
(
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If two events are mutually exclusive then (
same time.
)
since the two events cannot happen at the
Example: The product of rolling two dice
1. List the sample space for the products of rolling two dice.
2. Create a probability distribution for the product of two dice.
3. What is the probability that you would roll a product of 6 or a product of 8?
4. What is the probability that you would roll a product of 10 or a product of 12?
5. What is the probability that you would roll doubles or a product of 4?
Independent Practice: Flipping a Coin
1. List the sample space for flipping a coin four times.
2. Create a probability distribution for the number of tails you would flip.
3. What is the probability that you would flip at least 3 tails?
4. What is the probability that you flip at least 2 heads or at least 2 tails?