Question

Ten students were asked about how many hours each week they spent playing video games. These were their responses" 5,5,5,2,6,1,15,2,3,1

Calculate the Mean and show your work

Calculate the Median and show your work

Calculate the Mode and show your work

Answer 1

[AI-generated answer — Bot GPT 3.5]

Mean:

(5+5+5+2+6+1+15+2+3+1) / 10 = 45 / 10 = 4.5
Mean = 4.5

Median:
First, sort the data: 1, 1, 2, 2, 3, 5, 5, 5, 6, 15
Since there are 10 numbers, the median is the average of the two middle numbers:
(3 + 5) / 2 = 8 / 2 = 4
Median = 4

Mode:
The mode is the number that appears most frequently in the data set. Here, the number 5 appears three times, making it the mode.
Mode = 5

Answer 2

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 on 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 40

Answer 3

[AI-generated answer — Bot GPT 3.5]

To fill in the two-way table, we first identify the information provided in the problem:

20 classmates play video games and watch anime
9 classmates play only video games
8 classmates only watch anime
Thus, the information we have is:

- The total number of classmates is 40
- 9 classmates play only video games
- 20 - 9 = 11 classmates play both video games and watch anime
- 8 classmates only watch anime
- 20 classmates play on video games and watch anime
- 40 - 20 = 20 classmates who don't play video games or watch anime

Now, we fill in the two-way table:

Anime No anime Total
Video games 11 9 20
No Video games 8 20 28
Total 19 29 40

I hope this helps! Let me know if you need anything else.

Answer 4

Suppose that we randomly choose a student from class. Find the following probabilities:

P(Anime)
P(video games)
P(no anime)
P(no video games)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the probabilities, we first need to calculate the total number of students in each category. From the completed two-way table provided in the previous response:

- P(Anime) = (Number of students who watch anime) / (Total number of students)
P(Anime) = 19 / 40

- P(video games) = (Number of students who play video games) / (Total number of students)
P(video games) = 20 / 40

- P(no anime) = (Number of students who do not watch anime) / (Total number of students)
P(no anime) = 29 / 40

- P(no video games) = (Number of students who do not play video games) / (Total number of students)
P(no video games) = 28 / 40

Calculating the probabilities:

- P(Anime) = 19 / 40 = 0.475
- P(video games) = 20 / 40 = 0.5
- P(no anime) = 29 / 40 = 0.725
- P(no video games) = 28 / 40 = 0.7

Therefore,
P(Anime) = 0.475
P(video games) = 0.5
P(no anime) = 0.725
P(no video games) = 0.7

I hope this clears things up! Let me know if you have any further questions.

Answer 6

Now we will find some probabilities for two events occurring:

P(Anime and video games):
P(Anime and No video games):
P(Video games and no anime):
P(No video games and No anime)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the probabilities for two events occurring, we first need to calculate the number of students in each category from the two-way table:

- From the two-way table, the number of students who play video games and watch anime is 11.

- From the two-way table, the number of students who watch anime but do not play video games is 8.

- From the two-way table, the number of students who play video games but do not watch anime is 9.

- From the two-way table, the number of students who do not play video games and do not watch anime is 20.

Now, we can calculate the probabilities for each pair of events:

- P(Anime and video games) = (Number of students who play both video games and watch anime) / (Total number of students)
P(Anime and video games) = 11 / 40

- P(Anime and No video games) = (Number of students who watch anime but do not play video games) / (Total number of students)
P(Anime and No video games) = 8 / 40

- P(Video games and no anime) = (Number of students who play video games but do not watch anime) / (Total number of students)
P(Video games and no anime) = 9 / 40

- P(No video games and No anime) = (Number of students who do not play video games and do not watch anime) / (Total number of students)
P(No video games and No anime) = 20 / 40

Calculating the probabilities:

- P(Anime and video games) = 11 / 40 = 0.275
- P(Anime and No video games) = 8 / 40 = 0.2
- P(Video games and no anime) = 9 / 40 = 0.225
- P(No video games and No anime) = 20 / 40 = 0.5

Therefore,
P(Anime and video games) = 0.275
P(Anime and No video games) = 0.2
P(Video games and no anime) = 0.225
P(No video games and No anime) = 0.5

I hope this clarifies the probabilities for the pairs of events. Let me know if you need any further assistance.

Answer 8

Is P(Anime Or video games) = P(anime) + P(video games)? why or why not?

Answer 9

[AI-generated answer — Bot GPT 3.5]

The formula you presented, P(Anime OR video games) = P(Anime) + P(video games), is not correct for calculating the probability of the union of two events.

The correct formula for calculating the probability of the union of two events A and B (A OR B) is:

P(A OR B) = P(A) + P(B) - P(A AND B)

This formula accounts for the possibility of double-counting the probability of both events occurring at the same time (the overlap).

In this case, we are looking for the probability of a student playing video games OR watching anime. The events of a student playing video games and watching anime are not mutually exclusive (as shown by the number of students who do both), so we need to subtract the probability of both events occurring simultaneously.

Therefore, to calculate P(Anime OR video games), the correct formula is:

P(Anime OR video games) = P(Anime) + P(video games) - P(Anime AND video games)

The correct probability should be calculated as per the formula above. Let me know if you need further clarification or have any more questions.

Answer 10

make that shorter

Answer 11

[AI-generated answer — Bot GPT 3.5]

The formula P(Anime OR video games) = P(Anime) + P(video games) is not correct because it does not account for the overlap between the two events. The correct formula to calculate the probability of the union of two events A and B is:

P(A OR B) = P(A) + P(B) - P(A AND B)

This formula considers the possibility of double-counting when both events occur simultaneously.