Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up.
Sign up to join this community
What is the probability of receiving 1111 irrespective of what was
transmitted?
\$0.1^4 + 0.9^4 = 0.6562 \$
I am not sure about my answer because I think in my solution I am excluding the probability of getting 1111 as a combination of the two (0 or 1). I only assumed that the 1111 is a result of 0 being transmitted \$0.1^4\$ or 1 \$0.9^4\$.
Can anyone clarify this point to me?
I believe the answer can be derived as follows:
The probability of receiving 1111 is equal to the probability of transmitting a 1 taken to the fourth power. The probability of transmitting a 1 is equal to the sum of the probability of transmitting a 1 given the input is a 0 plus the probability of transmitting a 1 given the input is a 1. Based on your information that is equal to:
\$0.4 \cdot 0.1 + 0.6 \cdot 0.9 = 0.04 + 0.54 = 0.58\$
Thus the probability of receiving 1111 is \$0.58^4 = 0.1132\$
