R Programming for Biology - IT Assignment Help

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• Rationale: One of the important objectives of this course is to make you capable of carrying computational tasks using code that you have written. This involves both coming up with a method for completing the task and implementing this method in R. This assignment will require you to apply material covered in Units 2 and 3 to different contexts.

Question 1 - A standard deck of playing cards consists of 52 cards. These are divided into four suits (clubs, diamonds, hearts and spades). Clubs and spades are black in colour, whereas the other two suits are red. Each suit has 13 ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). J, Q and K are known as face cards. Use repeated simulation in R to answer parts a and b.

a. What is the probability that there is a face card among the top 11 cards in a well-shuffled deck?

b. What is the probability that at least two face cards are positioned next to each other in a well-shuffled deck?

Question 2 - a. Let n be a randomly chosen positive integer between 1 and Nmax (1 ≤ n ≤ Nmax). Write a function that takes Nmax as an input argument and returns the probability that the sum of digits of n (the randomly chosen integer) is strictly less than 5. Clarification: If n = 23, then the sum of digits of n is equal to 2 + 3 = 5. The digit sum of 23 is not strictly less than 5.

b. Using the function in part a, create a data frame with two columns. The first column, named Nmax should contain the numbers 10, 100, 1000, 10000, 100000, 1000000. The second column, named ‘Probability’ should contain the corresponding probability (the probability that the sum of the digits of a randomly chosen number between 1 and Nmax is less than 5). Finally, use the kable() function from the knitr package to format this data frame as a table in your PDF document (the desired table output is shown below, the ? should be replaced by the computed probabilities). Nmax Probability 10 0.5 100 ? 1000 ? 10000 ? 100000 ? 1000000 ?

Your submission should include the R code for parts a and b. You should also display the table specified in part b.

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