Question

The table summarizes the movie-watching preferences and ages of a group of 500 people in one community.


Movie Theater Streaming Service DVD
Under age 18 0.13 0.16 0.01
Age 18–40 0.17 0.17 0.06
Over Age 40 0.13 0.03 0.14


Part A: Determine P(DVD | age 18 to 40) and describe the event in everyday language. Show all work. (2 points)

Part B: Are the events prefers DVD and being age 18 to 40 approximately independent? Use probabilities to justify the answer. (2 points)

Answer 1

Step-by-step explanation:

Part A:

P(DVD | age 18 to 40) = P(DVD and age 18 to 40) / P(age 18 to 40)

Since it = 0.06 / 0.17

Then = 0.3529411764705882

In everyday language, this means that 35.29% of people who are 18 to 40 years old prefer to watch DVDs.

Part B:

The events prefers DVD and being age 18 to 40 are approximately independent if P(DVD and age 18 to 40) is close to P(DVD) x P(age 18 to 40).

P(DVD) = 0.06 + 0.16 + 0.14 = 0.36

P(age 18 to 40) = 0.17 + 0.17 = 0.34

P(DVD and age 18 to 40) = 0.06

P(DVD) x P(age 18 to 40) = 0.36 x 0.34 = 0.1224

Since P(DVD and age 18 to 40) is close to P(DVD) x P(age 18 to 40), the events prefers DVD and being age 18 to 40 are approximately independent.