A ternary string is a string consisting of 0s, 1s, and 2s. Suppose we are transmitting ternary strings through a

A ternary string is a string consisting of 0s, 1s, and 2s. Suppose we are transmitting ternary strings through a noisy communication channel with the following known probabilities:

• 0 is sent with probability 0.3

• 1 is sent with probability 0.4

• 2 is sent with probability 0.3

• Due to noise, 0 is changed to 1 during transmission with probability 0.2

• Due to noise, 0 is changed to 2 during transmission with probability 0.1

• Due to noise, 1 is changed to 0 during transmission with probability 0.2

• Due to noise, 1 is changed to 2 during transmission with probability 0.1

• Due to noise, 2 is changed to 0 during transmission with probability 0.2

• Due to noise, 2 is changed to 1 during transmission with probability 0.1

Suppose that a 1 is received. What is the probability that a 1 was sent?