0
\$\begingroup\$

enter image description here

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?

\$\endgroup\$

1 Answer 1

3
\$\begingroup\$

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\$

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.