Question

Your class of 40 students conducted a poll to determine who plays video games, who watches anime, who does both, and who does neither. Here are the results:

• 20 Classmates play video games and watch anime
• 9 Classmates play only video games
• 8 Classmates only watch anime
Use the class data to fill in the two-way table
Anime. No anime. Total
Video games
No video games
Total

Suppose that we randomly choose a student from class. Find the following probabilities:
P(Anime):
P(No Anime)
P(Video Games):
P(No Video Games):
Now we will find some probabilities for two events occurring:
P(Anime & Video Games):
P(Anime & NoVideo Games):
P(Video Games & No Anime):
(Video Games & No Anime):
P(NoVideo Games & No Anime):

Is P(Anime OR Video Games) = P(Anime) + P(Video Games)? Why or Why Not?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To fill in the two-way table:

Anime. No anime. Total
Video games 20 9 29
No video games 8 3 11
Total 28 12 40

Now, let's find the probabilities:

P(Anime) = (20 + 8) / 40 = 28 / 40 = 0.7
P(No Anime) = (9 + 3) / 40 = 12 / 40 = 0.3
P(Video Games) = (20 + 9) / 40 = 29 / 40 = 0.725
P(No Video Games) = (8 + 3) / 40 = 11 / 40 = 0.275

For the probabilities of two events occurring:

P(Anime & Video Games) = 20 / 40 = 0.5
P(Anime & No Video Games) = 8 / 40 = 0.2
P(Video Games & No Anime) = 9 / 40 = 0.225
(Video Games & No Anime) = 20 / 40 = 0.5
P(No Video Games & No Anime) = 3 / 40 = 0.075

P(Anime OR Video Games) = P(Anime) + P(Video Games) - P(Anime & Video Games) = 0.7 + 0.725 - 0.5 = 0.925

Therefore, P(Anime OR Video Games) is not equal to P(Anime) + P(Video Games). This is because we need to subtract the probability of both events occurring in order to avoid double counting.