1) Student Sam has access to two types of internet connection: a 4G phone connec
ID: 3332965 • Letter: 1
Question
1) 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) If Sam failed to submit an assignment, what is the probability that the WiFi connection was not working, given the probability of Sam not submitting an assignment is 0.38?Explanation / Answer
Here we are given that:
P( fail | no wifi ) = 0.9 that is the probability that he will fail to submit given that wifi does not work
P( fail | out of data ) = 0.95 that is the probability that he will fail to submit given that 4g is out of service
Also, we are given that:
P( no wifi ) = 0.3 and P( out of data ) = 0.25
a) Probability that there would be at least one thing working - either wifi or 4g data
= 1 - Probability that both are not working
= 1 - (1 - P( no wifi ) )*(1 - P( out of data ) )
= 1 - (1 - 0.3)*(1 - 0.25 )
= 0.475
Therefore 0.475 is the required probability here.
b) Given that he failed to submit the assignment, probability that wifi was not working is computed as:
= Probability that wifi is not working and he failed to submit the assignment / Probability that he failed to submit the assignment
= P( no wifi )P( fail | no wifi ) / 0.38
= 0.9*0.3 / 0.38
= 0.7105
Therefore 0.7105 is the required probability here.
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