Student Sam has access to two types of internet connection: a 4G phone connectio
ID: 2922264 • Letter: S
Question
Student Sam has access to two types of internet connection: a 4G phone connection, and a WiFi
connection. The WiFi has unlimited data but is very unstable. The 4G connection is very stable but has
limited data available. It is Friday night and Sam must submit an MZB126 assignment, there is a 90%
chance that Sam will fail to submit their assignment if the WiFi isn't working and a 95% chance that Sam
will fail to submit their assignment if the 4G service is out of data. Given that the probability of the WiFi
not working 30% and the probability his 4G service is out of data is 25%
a) What is the probability that Sam will have at least one way to submit their assignment, i.e. either the
WiFi or the 4G connection will be working?
b) Calculate the probability that Sam fails to submit their assignment.
c) If Sam failed to submit an assignment, what is the probability that the WiFi connection was not
working?
Explanation / Answer
Two types of internet connection:
a 4G phone connection, and a WiFi connection
Let say events
Wifi not working = A
4G data not working = B
same wil sfail to submit the assignment =C
Pr(Same will fail to submit the assignment l wifi not working) = Pr(C l A) = 0.90
Pr(Sam will fail to submit the assignment l 4G phone not working) = Pr(C l B) = 0.95
Pr(Wifi not working) = P(A) = 0.30
Pr( 4G service not working) = P(B) = 0.25
(a) What is the probability that Sam will have at least one way to submit their assignment, i.e. either the WiFi or the 4G connection will be working.
Pr(at least one internet connection is working) = 1 - Pr( both mobile data and 4G service in not working)
= 1 - 0.3 * 0.25 = 0.925
(b) probability that Sam fails to submit their assignment.
P(C) = P(C l B) * P(B) + P(C l A) * P(A) = 0.90 * 0.30 + 0.95 * 0.25 = 0.5075
(c) probability that the WiFi connection was not working if sam failed to submit an assignment
Pr( wifi connection was not working l sam failed to sumbit an assignment) = (0.90 * 0.30)/ ( 0.90 * 0.30 + 0.95 * 0.25) = 0.532