A pair of fair dice are tossed together and independently 9 times and a match re

Question

A pair of fair dice are tossed together and independently 9 times and a match recorded each time they show the same value. Let X be the number of matches in the 9 trials. (a) What is EX? (b) What is VarX? (c) What is the probability that at least one match appears in the 9 trials? Now with the same dices if two fair dice are tossed together repeatedly until they show a match . Let N be the number of the pair-toss on which this happens. (a) What is EN? (b) What is VarN? (c) What is the probability that 4 or more pair-tosses are needed to get a match?

Explanation / Answer

(i) The number of successes is greater than the number of failures means that you have more than 9 successes. Therefore you have to add the probability of having 10, 11, ..., 18 together.()()10()8+()()11()7+...+()()18()0(ii) The number of successes is twice as large as the number of failures is same as finding the probability of having 12 successes. This is due to the fact that you are rolling the fair die 18 times and in order to have twice the amount of successes than failures, the only possible

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