1. Let A = You get an A in this course. Let S = You study hard. Translate Pr(A |S) into a sentence. (1 pt.)

2. Provide the formula for the following conditional probability. (1 pt.)

Pr(A | B) =

3. Determine the probability values for the following scenario. (8 pts.)

Schylling and Astro are two of the top manufacturers of lava lamps. Three percent of Schylling Lava Lamps fall below quality standards, while six percent of Astro Lava Lamps are below quality standards. A retro shop in town buys 40% of its lava lamps from Schylling and 60% of its lava lamps from Astro.

Let A = Astro, S = Schylling, D = Defective.

Draw a tree diagram representing all the possible outcomes of this scenario and their probabilities.

Pr(A) = Pr(S) =

Pr(D |A) = Pr(D | S) =

Pr(~D | A) = Pr(~D | S)

Pr(D) =

What is the probability that a lava lamp in the shop taken at random and found to be below quality standards was manufactured by Astro? In other words, what is the Pr(A | D)?