Question

pls show work not on excel ! will given good review

Exercise 3.3. Suppose we roll 2 fair, 20-sided dice, each with faces numbered 1 through 20. What is the probability that the sum of the numbers rolled is divisible by 2 or 3?

Exercise 3.5. Building on the previous exercise, suppose again that n ∈ N and that k is an integer with 0 ≤ k ≤ n. Suppose also that p ∈ [0, 1] and that we have a (possibly biased) coin which flips heads with probability p. If we flip this coin n times, what is the probability of flipping exactly k heads?

Exercise 3.6. Consider the probability space (S, E, P) constructed in our darts problem, Example 3.3.1. What is the probability that our dart will strike the dartboard at a point closer to the point (0, 0) than to the point (1/2, 0)?

Answer 1

no of Favourable = 268 Total number of events n = 400

The probability that the sum of the numbers (x+y) rolled divisible by 2 or 3 p̂ = 268/400 = 0.67