conditional probability. the probability that event, b, will occur given that another event, a, has...
TRANSCRIPT
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Conditional Probability
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Conditional Probability
The probability that event, B, will occur given that another event, A, has already happened.
Exists when two events depend on each other.
𝑃 (𝐵∨𝐴)
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1. Re-write each conditional probability into words:
a. P(have short hair | the person is a boy)
b. P(taking Spanish | senior)
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Tree Diagrams
Splits into two branches off each branch
Two branches must add up to 1 (100%)
Start with the item that all other items DEPEND
on
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1. A car insurance company compiled the following information from a recent survey.
75% of drivers carefully follow the speed limit. Of the drivers who carefully follow the speed limit, 80% have
never had an accident. Of the drivers who do not carefully follow the speed limit,
65% have never had an accident.
a. Make a tree diagram based on the information above.
b. What is the probability that a driver does not carefully follow the speed limit and has never had an accident?
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2. A softball game has an 80% chance of being cancelled if it rains and a 30% chance of being cancelled if there is fog when there is no rain. There is a 70% chance of fog with no rain and a 30% chance of rain.
a. Make a tree diagram based on the information above.
b. Find the probability that there will be fog and the game will be cancelled.
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a. P(J and U)
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b. P(E)
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4. The population of a high school is 51% male. 45% of the males and 49% of the females attend concerts.
a. Make a tree diagram based on the information above.
b. Find the probability that a student is female and does not attend concerts.
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5. A football team has a 70% chance of winning when it doesn’t snow, but only a 40% chance of winning when it snows. Suppose there is a 50% chance of snow.
Make a tree diagram Find the probability that the team will win.