Conditional Probability

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)

1. Re-write each conditional probability into words:

  a. P(have short hair | the person is a boy)

b. P(taking Spanish | senior)

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

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?

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.

a. P(J and U)

b. P(E)

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.

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.