*Project Instructions *

In this project, you will use R to solve counting and probability problems. To gain the most benefit from this project, avoid calculating numeric values and entering them into R. Instead, use R to do all necessary calculations.

*Setting up Your Project *

When working in RStudio, be careful with cloud drives. RStudio does not always play well with cloud drives’ longer file path names. You will be best served by using a local drive whenever possible until you are comfortable troubleshooting technical issues.

Create a new project called “Lastname-Project5”.

Create an R Script file within your project called “Lastname-Project5.R”.

Include your name, the date, and the class in a comment as the first line of the script.

Include any script initialization code and library loading.

*Testing Your Solution *

You can evaluate your project using the project5_tests.R test file. This will only work if you store results in the exact variable names specified in bold and in parentheses at the end of the problem.

*Problems*

Using the ball-dataset.

1. Download the data set ball-dataset.csv and read it into your script. Each ball in the dataset is represented by a color (red, blue, green, or yellow) and a label (A, B, C, D, or E).

2. Create a frequency table as a data.frame or tibble that contains counts for each color of ball (freq_color).

3. Create a frequency table as a data.frame or tibble that contains counts for each label of ball (freq_label).

4. Create a bar chart of the ball data set representing the counts of the different colors.

5. Create a bar chart of the ball data set representing the counts of the different labels.

6. What is the probability of drawing a green ball (prob6_result)?

7. What is the probability of drawing a blue or a red ball (prob7_result)?

8. What is the probability of drawing a ball with a label of A or C (prob8_result)?

9. What is the probability of drawing a yellow ball with a D (prob9_result)?

10. What is the probability of drawing a yellow ball or a ball with a D (prob10_result)?

11. What is the probability of drawing a blue ball followed by a red ball without replacement (prob11_result)?

12. What is the probability of drawing four green balls in a row without replacement (prob12_result)?

13. What is the probability of drawing a red ball followed by a ball with a B without replacement (prob13_result)?

14. [Challenge] Write the factorial function that computes the factorial of a given number.

– Recall that factorial (0) = 0

– factorial(3) = 6

– factorial(5) = 120

– For this problem you should handle all negative inputs as returning the value -1.

• factorial(-10) = -1.

*Creating a coin flipping data frame*

For the following problems, consider an unfair coin that has a probability .6 of landing on heads.

18. Manually create a data.frame or tibble that contains all possible outcomes of flipping the coin four times (coin_outcomes).

19. Compute the probability of each row outcome and store it as a column in the data.frame or tibble. You can do this manually or programmatically (coin_outcomes).

20. There are 5 possible outcomes in our coin dataset if we count the number of heads in each row. For example, the row “H H H H” has 4 heads and the row “H T H T” has 2 heads. Compute the probability of each of the 5 possible outcomes (num_heads_prob).

21. What is the probability of an outcome of three heads (prob21_result)?

22. What is the probability of an outcome of two heads or four heads (prob22_result)?

23. What is the probability of an outcome of less than or equal to three heads (prob23_result)?

24. Create a bar chart where the x-axis is the outcome and the y-axis is the probability.

*Soccer Games (Optional Challenge Problems)*

The following problems consider a soccer team with a 75% chance of winning a game at home and a 50% chance of winning away games. Consider that the team is about to play 10 games: five at home and five away.

25. What is the probability that they will win exactly 10 games (prob25_result)?

26. What is the probability that they will win more than one game (prob26_result)?

27. How many different ways could you pick five games at random and have three home games and two away games (prob27_result)?

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