Finding Conditional Probability in Models Practice Test

A class has 10 students. Each student is equally likely to be selected at random.

The students are:

• Soccer: Ana, Ben, Cam, Dee
• Basketball: Eli, Fay, Gus
• Neither: Hal, Ivy, Jay

Let event $A$ be “the selected student plays soccer” and event $B$ be “the selected student plays a sport (soccer or basketball).”

Using the list above, what is $P(A\mid B)$? Give your answer as a simplified fraction.

A two-step experiment is performed: first choose a letter from {X, Y} and then choose a number from {1, 2, 3}. All 6 outcomes are equally likely.

The outcomes are: {X1, X2, X3, Y1, Y2, Y3}.

Let event $A$ be “the outcome has number 1” and event $B$ be “the outcome starts with Y.”

From the outcomes listed, what is $P(A\mid B)$? Give your answer as a simplified fraction.