# GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 4

Probability of sending a 1 is 1/3, with probability of being received correctly 0.8. Probability of sending a zero is 2/3, with probability of being received correctly 0.9.

Which of the following option is correct ?
(A) 2/3 is the probability that a 0 is received.
(B) 0.9 is the probability that a 0 was transmitted given that a 0 was received.
(C) Both (A) and (B)
(D) None of these

Explanation: Find the probability that a 0 is received.
A received zero is either a correct zero or an incorrect 1, so by the Sum Rule the probability is

`(1/3)(0.2) + (2/3)(0.9) = 2/3 `

Find the probability that a 0 was transmitted given that a 0 was received.
By Bayes’ Theorem the probability is,,

`(2/3)(0.9)/(2/3) = 0.9 `

So, option (C) is correct.

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