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

@aubree

Answer 2

One min. I acadently deleted what I was typing

Answer 3

That's alright,t ake your time!

Answer 4

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.

Answer 5

Oh I think I did it wrong, mind if I put what I did?

Answer 6

I uh put... Part A:

Probability of being P(DVD and Ages 18 to 40) = 0.17 + 0.17 + 0.06 = 0.4

So, our probability of preferring DVDs among those aged from 18 to 40 should be P(Ages 18 to 40) - 0.06.

P(DVD| Age 18 to 40) = P(DVD and age 18 to 40)/P(Age 18 to 40) = 0.06/0.4 = 0.15

Part B:

P(DVD) = 0.01 + 0.06 + 0.14 = 0.21

From Part A P(DVD| Ages 18-40) = 0.15

So, since P(DVD| Ages 18 to 40) is not approximately equal to P(DVD), the events are not approximately independent.

This means our answer is that no the events prefers DVD, and being ages 18 to 40 are not independent because P(DVD| Ages 18 to 40) is not approximately equal to P(DVD).

Answer 7

Uh, yea, that's fine

Answer 8

Is it correct?

Answer 9

Yea, for the most part

Answer 10

Oh, I was worried I did it wrong when I saw yours TwT