A dice game consists in rolling a fair six-sided die: the roll is considered as success only when side four or 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:
a. Probability of success
b. Probability of loss
2-Assuming that the die rolls are independent, what is the distribution (type and parameters) of the number of trials until realizing 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 conditional probability 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 your findings