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#1




Question 168 on the SOA's Study Guide
Hello,
I have a question concerning mutual independence and independence. The question is as follows... Two fair dice, one red and one blue, are rolled. Let A be the event that the number rolled on the red die is odd. Let B be the event that the number rolled on the blue die is odd. Let C be the event that the sum of the numbers rolled on the two dice is odd. Determine which of the following is true. (A) A, B, and C are not mutually independent, but each pair is independent. (B) A, B, and C are mutually independent. (C) Exactly one pair of the three events is independent. (D) Exactly two of the three pairs are independent. (E) No pair of the three events is independent. On the SOA's answers, it says events A,B, and C all have a 0.5 probability; however, isn't the probability of event C happening less than 0.5 since the sum of the dice can only take values between 2 and 12 (there would be a 5/11 chance of getting an odd sum)? This would change the answer. Please let me know if I am thinking about this wrong. 
#2




No, the total possible combination is 36 (6 possible outcomes on first die x 6 possible on second die). Therefore, the possibility of getting a sum of 2 is 1/36 (1 on first die, 1 on second die), sum of 3 is 2/36 (1/2 or 2/1) and so on... therefore, the possibility of odd sum is 18 out of 36 outcomes and the same for even sums.
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independence, probability 
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