probability

Question

For certain binary communication channel probability transmitted 0 is received as o is 0.95 and probability that transmitted 1 is received as transmiited 1 is 0.9 If probability 0 is transmiited is 0.4 find probality that 1 was transmitted given 1 was received?

Answer 1

P(0T)= 0.4 ie probability of 0 transmitted.

P(1T) = 0.6

P(1R) = probability of receiving 1.

case 1 :if 0 is transmitted than we can receive it as 1

case 2 : if 1 is transmitted than we can receive it as 1

P(1R) = 0.4*(1-.95) + 0.6 *.90 = .56

P(1T $\bigcap$ 1R) = 0.6*.9=.54

P(1T/1R) = .54/.56 = 0.96