My Math Forum Tree Diagram and Dependent probability.

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 December 7th, 2017, 05:04 AM #1 Newbie   Joined: Dec 2017 From: London Posts: 3 Thanks: 0 Tree Diagram and Dependent probability. Hi so I need some help with this question? Following a survey, it is found that a train service in Japan is late 2% of the time. For a particular working week of 5 days, a passenger wishes to investigate the potential lateness of the train service. a) Find the probability that the train is not late on any of the 5 days. [3] b) Calculate the probability that the train is late on fewer than two days. [3] c) If the train is late on between two and three days, customers who purchased a weekly train pass are offered a half-refund. Calculate this probability. [4] d) However, if the train is late on four or more days, customers purchasing a weekly train pass are offered a free pass for the following week. Calculate the probability of this occurrence. [2] any help is greatly appreciated! Last edited by DecoMate; December 7th, 2017 at 05:25 AM. Reason: new question
 December 7th, 2017, 04:03 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,757 Thanks: 900 I guess they want you to model this as a binomial distribution with $n=5,~p=0.02$ $P[k]=P[\text{train is late k days out of 5}]=\dbinom{5}{k}p^k(1-p)^{5-k}$ a) $P[\text{train late 0 of 5 days}] = P[0] = (0.8 )^5$ b) $P[\text{train is late < 2 days}]=P[0]+P[1]$ c) $P[\text{half refund}] = P[2]+P[3]$ d) $P[\text{free pass for next week}] = P[4]+P[5]$

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