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December 7th, 2017, 04:04 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 halfrefund. 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 04:25 AM. Reason: new question 
December 7th, 2017, 03:03 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,039 Thanks: 1063 
I guess they want you to model this as a binomial distribution with $n=5,~p=0.02$ $P[k]=P[\text{train is late k days out of 5}]=\dbinom{5}{k}p^k(1p)^{5k}$ 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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