# 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**Answer:** **(C)****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 Bayesâ€™ Theorem the probability is,,

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

So, option (C) is correct.

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