Show all the necessary steps as clear as possible ( \( 15 \% \) ) 1) In a binary communication system, a ' 0 ' and a ' 1 ' is transmitted with probability 0.6 and 0.4 respectively. Due to an error occurring in the communication system, a ' 0 ' becomes a ' 1 ' with a probability of 0.1 , and a ' 1 ' becomes a ' 0 ' with a probability of 0.08 . Find a) The probability of receiving a ' 1 ' b) The probability of receiving a ' 0 ' c) The probability that a ' 1 ' was transmitted when the received message is ' 1 '.
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The probability of transmitting a '1' and receiving it correctly is the product of the probability of transmitting a '1' and the probability of receiving a '1' given that a '1' was transmitted. This is 0.4 * (1 - 0.08) = 0.4 * 0.92 = 0.368. The probability of Show more…
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