Question

The table summarizes the daily caffeine habits and majors of students at one university.


Coffee Energy Drink No Caffeine
STEM Major 0.32 0.13 0.02
Not STEM Major 0.17 0.27 0.09
Part A: Determine P(energy drink | STEM major) and describe the event in everyday language. Show all work. (5 points)

Part B: Are the events consuming energy drinks and a STEM major approximately independent? Use probabilities to justify the answer. (5 points)

Answer 1

@toga

Answer 2

Part A:
To determine P(energy drink | STEM major), we need to use conditional probability formula:
P(energy drink | STEM major) = P(energy drink and STEM major) / P(STEM major)

From the table, we can see that the probability of students being STEM major is 0.32 + 0.13 + 0.02 = 0.47.
The probability of STEM major students consuming energy drinks is 0.13.
Therefore, P(energy drink and STEM major) = 0.13.
Putting these values in the formula, we get:
P(energy drink | STEM major) = 0.13 / 0.47 = 0.2766 (rounded to four decimal places).

The event described in Part A is that a randomly selected student who is a STEM major consumes an energy drink.

Part B:
To determine if the events consuming energy drinks and a STEM major are approximately independent, we need to compare the joint probability of these events with the product of their individual probabilities. If the joint probability is close to (or equal to) the product of individual probabilities, then we can say that the events are approximately independent.

Let's calculate the joint probability of these events:
P(energy drink and STEM major) = 0.13 (from the table)

Now let's calculate the product of their individual probabilities:
P(energy drink) * P(STEM major) = 0.13 + 0.27 + 0.09 * 0.32 + 0.17 + 0.09 = 0.13

Since the joint probability is equal to the product of their individual probabilities, we can say that the events consuming energy drinks and a STEM major are approximately independent.

Answer 3

this my favorite question today

Answer 4

Me on a daily basis except I'm in statistics not stem and constantly tired

Answer 5

I get it lol

Answer 6

I seriously hope the majority of these questions are right toga, I can't afford to fail sob

Answer 7

But you usually get me and 80 or so-

Answer 8

I mean it's at a 56 so far without the written ones being graded so :]

Answer 9

Lookin good so far, I'll let you know how the written ones score ty for your help!

Answer 10

(Seriously I would probably be failing without you)

Answer 11

I really would