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This question is incomplete, the complete question is;
Assume that the probability of error-free transmission of a message over a communication channel is p=0.9. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called a feedback channel. Assuming that successive transmissions are independent, what is the probability that:
a) No retransmission is required.
b) Exactly two retransmissions are required
Answer:
a) probability that No retransmission is required is 0.90
b) the probability that exactly two retransmissions are required is 0.009
Step-by-step explanation:
Given the data in the question;
the probability of error-free transmission of a message over a communication channel is p = 0.9
a) probability that No retransmission is required will be;
Let x represent the error-free transmission of a message
Now, the P( error-free_transmission_of_a_message) = 0.90
so;
P( X=0 ) = 0.90( 1 - 0.90 )⁰
P( X=0 ) = 0.90( 0.1 )⁰
P( X=0 ) = 0.90( 1 )
P( X=0 ) = 0.90
Therefore, probability that No retransmission is required is 0.90
b) Probability that exactly two retransmissions are required will be;
P( X=2 ) = 0.90( 1 - 0.90 )²
P( X=2 ) = 0.90( 0.1 )²
P( X=2 ) = 0.90( 0.01)
P( X=2 ) = 0.009
Therefore, the probability that exactly two retransmissions are required is 0.009