Question 4. Consider the following scenario: Let P(C) = 0.2. Let P(D) = 0.3. Let P(C|D) = 0.5. (a) Find P(C n D). (b) Are C and D mutually exclusive? Why or why not? (c) Are C and D independent events? Why or why not? (d) Find P(C u D). (e) Find P(D|C). Question 1. An unfair die is tossed. Determine which of the following assignments could be made for the probabilities of each simple outcome. If an assignment cannot be made, tell why. (a) P(1) = 0.3,P(2) = 0.2,P(3) = 0.3,P(4) = 0.1,P(5) = 0.3,P(6) = 0.4 (bi P(1) = 0,P(2) = D.2,P(3) = 0.3,P(4) = 0.1,P(5) = 05,1903) = 0.1 (c) P(1) = 0.1,P(2) = 0.2,P(3) = 0.3. 13(4) = 0.1,P(5) = 0.1.P(6) = 0.2 Question 2. If we roll a fair die twice, (a) What is the sample space? (b) what is the probability that the total sum is 5? (Write the event as well) is) what is the probability that the total sum is less than 5? (Write the event as well) id} What is the probability of obtaining two even numbers? (Write the event as well) le) what is the probability that the total sum is more than 12? (Write the event as well] Question 3. This table shows a random sample of 100 hikers and the areas of hiking they prefer. Calculate the following probabilities using the table. (a) Find the probability that the hiker prefers to hike on the coastline. (b) Find the probability that the hiker is female and prefers to hike near lakes and streams. (c) Find the probability that the hiker is female or prefers to hike near lakes and streams. (d) Find the probability that the hiker is male or prefers to hike on mountain peaks. to) Find the probability that the hiker is male given he prefers to hike on mountain peaks. if) Find the probability that the hiker is female given she prefers to hike on the coastline. lg] Find the probability that the hiker prefers to hike on the coastline given she is female. (h) Let M = being male, and let L = prefers hiking on mountain peaks. Are M and L independent? Are M and L mutually exclusive