Conditional Probability and OJ Simpson

His defense lawyer said in court…

Do you see the difference?

NOTATION

Orunion

(use addition)

AndIntersection

(use multiplication)

TREE DIAGRAMSHOW ALL THE POSSIBLE INTERSECTIONS OF EVENTS

Make a tree for the following situation:You know the answer yon a test 75% of the time and when you know the answer you always get it right, but when you don’t know the answer and you guess you only get the answer right 20% of the time.

Conditional Probability

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BP

BAPBAP

and

Use this when we have additional information

1% of the population has disease X.

If someone has the disease and gets tested the test is positive every time.

If a healthy person gets tested for disease X they will get a false positive 10% of the time.

1. If we randomly choose a person what is the probability that the test will be positive?

2. If the lab comes back positive what will be the probability the person actually has the disease?

Suppose a voter poll is taken in three states.

State A: 50% voters support the liberal candidate State B: 60% voters support the liberal candidate State C: 35% voters support the liberal candidate.

Of the total population of the three states40% live in state A25% live in state B35% live in state C.

Given that a voter supports the liberal candidate, what is the probability that she lives in state B?