My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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
DecoMate is offline  
 
December 7th, 2017, 04:03 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,652
Thanks: 838

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) $P[\text{free pass for next week}] = P[4]+P[5]$
romsek is online now  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
dependant, dependent, diagram, probability, tree



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
sets and dependent probability officerwhiskers Probability and Statistics 1 March 18th, 2015 12:32 PM
probability tree Trishyliz Probability and Statistics 0 March 5th, 2015 01:45 PM
Use a tree diagram to calculate the probability alfred_oh Advanced Statistics 0 May 3rd, 2013 07:43 AM
Deriving formula from tree diagram? Wevans2303 Advanced Statistics 0 October 30th, 2011 02:07 PM
how to solve this tree diagram problem limengxi Advanced Statistics 1 March 9th, 2011 01:49 AM





Copyright © 2017 My Math Forum. All rights reserved.