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# A dice game consists in rolling fair six-sided die: the roll is considered as success only when side four O side five (face N 4 or Face N 5) is on top, otherwise t...

## Question

###### A dice game consists in rolling fair six-sided die: the roll is considered as success only when side four O side five (face N 4 or Face N 5) is on top, otherwise the die roll is considered as failure.1-Calculate (with justification) the following: Probability of a success Probability of a loss 2-Assuming that the die rolls are independent; what is the distribution (type and parameters) of the number of trials until getting the first success?3-What is the expected number of trials until the firs

A dice game consists in rolling fair six-sided die: the roll is considered as success only when side four O side five (face N 4 or Face N 5) is on top, otherwise the die roll is considered as failure. 1-Calculate (with justification) the following: Probability of a success Probability of a loss 2-Assuming that the die rolls are independent; what is the distribution (type and parameters) of the number of trials until getting the first success? 3-What is the expected number of trials until the first success? 4-What is the probability to win at most after 2 trials? 5-What is the probability to win at most after 3 trials? 6-Use_the_conditionalprobability rule to find the probability to win at most after 5 trials giving that no success is observed in the first three trials? 7-Compare the results of (6) and (4), comment on this

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