1. (a) Two six-sided dice are rolled. Let A be the event that sum of two dice equals to 3. Let B be the event that sum o

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1 A Two Six Sided Dice Are Rolled Let A Be The Event That Sum Of Two Dice Equals To 3 Let B Be The Event That Sum O 1 (56.19 KiB) Viewed 77 times

1. (a) Two six-sided dice are rolled. Let A be the event that sum of two dice equals to 3. Let B be the event that sum of two dice equals to 7. Let C be the event that at least one of the dice shows a 1. i. What is the conditional probability P(AC)? (5 marks) ii. What is the conditional probability P(BIC)? (5 marks) iii. Are A and C independent? Are B and C independent? (5 marks) (b) Suppose a biased coin with probability p of heads is tossed, while a fair coin is tossed at the same time. Let X be the number of tosses until both coins simultaneously show the same outcome. i. What is the probability distribution of X? (6 marks) ii. Compute the expected value and standard deviation of X? (4 marks)