Question

Consider data transmission between two computers in different geographical locations. Data is transmitted in ‘blocks’, that is, in fixed-length sequences of digits. Suppose that the transmission may be routed over any one of three different routes, the selection being made automatically by a route selector according to existing traffic conditions, every time transmission of a block is initiated. Transmission takes place over the three routes various fractions of the time, as follows:
Route A: 60% of the time
Route B: 30% of the time
Route C: 10% of the time
Transmission errors can occur that render a block completely useless. The probability of a block experiencing such an error depends on the route. It is
0.001 when route A is used
0.002 when route B is used
0.003 when route C is used.
What is the probability that an error, when it does occur, arises on route C?

Answer 1

This question can be solved by Bayes Theorem

Let E represent the event of a transmission error.

We are given:

P(A) = 0.60

P(B) = 0.30

P(C) = 0.10

P(E/A)= 0.001

P(E/B) = 0.002

P(E/C) = 0.003

We have to calculate the probability P(C/E)

We know by the definition of conditional probability:

Using Bayes theorem:

The required probability is 20%.

If satisfied, please do upvote! Let me know in the comments if anything is unclear. I will reply ASAP