Question

Question 6: Winston, a dog, loves to play fetch. He catches each ball mid-air independently with probability 0.4. Write a simulation in R in which you throw Winston five balls and compute how many of the five balls he catches mid-air. Repeat this simulation N=5,000 times.

a) Plot a histogram of the number of catches Winston has made in each series of five catches.

b) What proportion of the time does Winston catch exactly two balls mid-air?

c) What proportion of the times does Winston catch exactly three balls mid-air?

d) Can you derive a formula to describe the probability of catching X=0,1,2,3,4,5 balls mid-air? How well does this formula match the proportions in your histogram? Hint: You will need to use the Combination Rule for (d).

Answer 1

value obtained through probability model are on an average close to values obtained from histogram