If you can finish this within an hour I will give you a very good rating!

Question #1 [12 marks] Recall from Question #3, Lab Report 1, the popular casino game Roulette where a ball spins on a circular wheel and lands on one of the numbers 00, 0, 1, 2, 3, . . . ,36 (Le. there are 38 numbers on the wheel). Each of the numbers also takes on one of the colours green, red, or black. Consider the following events: Event A : {ball lands on a \"red\" number} Event B: {ball lands on an \"odd\" number} = {1, 3, 5, 7, . . . , 35} Note: In Roulette, {1,3,5, . . ,35} are considered odd numbers, {2,4, 6, 8, . . . , 36} are considered even numbers, and {0,00} are considered neither even nor odd. So, 3' is not an even number (it's a non-odd number). 9 9 5 a. Given that P(A) = E' P(B) = E' and P(An B) = E' use this information and probability formulas to determine each of the following probabilities as exact values. Be sure to show the formulas used and interpret each result. i. P(A u B) ii. P(B ' n A) iii. P(A' n B ') iv. P(BlA u B) b. Are events A and B i) mutually exclusive? ii) independent? Provide a mathematical explanation with each