The Por Mano Tile Company imports handmade tiles from Mexico

The Por Mano Tile Company imports handmade tiles from Mexico. “Saltillo” tiles make up 67% of their imports and the rest are “talavera” tiles. Based on past experience, they expect 3.7% of the Saltillo tiles arrive broken and 5.4% of the talavera tiles to be broken. In each question below assume we are drawing a single tile from a batch of imports. (3 points each) a. Find the probability that a tile is a talavera tile and is broken. b. Find the probability that a tile is not broken. c. Find the probability that a Saltillo tile is broken. d. Find the probability that a talavera tile is not broken.

Solution

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

Probability that a tile is a talavera tile = 1 - 0.67

probability that a tile of talavera tiles is broken = 0.054

0.054 * (1-0.67 ) = 0.01782

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

Probability that a tile is not broken = 1 - Probability that a tile is broken

Probability broken = 0.67 * 0.037 + (1-0.67) * 0.054 = 0.04261

Probability that a tile is not broken = 1 - 0.04261 = 0.95739

. Find the probability that a Saltillo tile is broken.

Probability = 0.67 * 0.037 = 0.02479

Find the probability that a talavera tile is not broken.

probability = (1-0.67) * ( 1 -0.054 ) = 0.31218