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Question: the class is egen 350 pleas i need the answers...

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the class is EGEN 350 pleas i need the answers of questions 12,13 and 14

12, A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Defeating any opponent is independent of previous encounters. In the game, the player continues to contest opponents until the player is defeated. The random variable X is how many opponents are contested until the player is defeated. [Think: what is the success in this case?] a. (3pts) What is the probability mass function of the number of opponents the player contests in a game, i.e. what is the pmf equation involving x? b. (3pts) What is the probability that a player defeats at least 2 opponents in a game? [Think: If the player defeats 2 opponents, then how many opponents did the player contest in a game?] 13. (3pts) A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 12 invoices are sampled at random. What is the probability that fewer than 3 of the 12 sampled invoices receive the discount? 14. A state runs a lottery in which 6 numbers are randomly selected from 40, without replacement. A player chooses 6 numbers before the state chooses its 6 numbers. A player wins if the players 6 numbers match all 6 of the states numbers. a. (3pts) What is the probability of the player winning, in other words, the probability that the players 6 numbers exactly match the states 6 numbers? b. (3pts) What is the probability that O of the 6 numbers chosen by a player appear in the states sample?

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