### MAT 142 3.6 Conditional Probability and Intersections

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MAT 142 Problem set

Unit: Probability

Topic: Conditional Probability and Intersections

Directions: Solve the following problems. Please show your work, use proper notation, and explain your

reasoning.

1. The Por Mano Tile Company imports handmade tiles from Mexico. Saltillo tiles makes up 67%

of their imports and the rest are talavera tiles. Based on past experience, they expect 3.7% of

the Saltillo tiles to arrive broken and 5.4% of the talavera tiles to be broken.

a. Make a complete probability tree for this situation.

b. Find the probability that a tile is a talavera tile and is broken

c. Find the probability that a tile is not broken.

d. Find the probability that a Saltillo tile is broken.

e. Find the probability that a talavera tile is not broken

1. The results of the October 3rd vote on the Emergency Stabilization Act of 2008 are shown in the

table below.

Region Yes No Totals

Midwest 57 42

Northeast 62 21

South 86 68

West 58 40

Total 263 171

1. Find the probability that a congressman voted for no

2. Find the probability that a congressman was from the west and voted yes.

3. Find the probability they voted yes given that they were from the west

4. Find the probability that they were Midwestern if they voted no.

5. Find the probability that a congressman voted no if they were from the South or West.

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