A zero received

Topic: Random experiments and probability · more questions on this topic
‹ A one received on a noisy channel Information about one die ›

Zeros and ones are sent with equal probability. A sent 0 is received as 0 with probability 0.95, and a sent 1 is received as 1 with probability 0.99. A 0 is received. Find the probability that a 1 was sent.

Worked answer (click to show)

Let B be the event that a 1 was sent and A the event that a 0 was received. Then \mathbb{P}(A\mid B)=0.01, \mathbb{P}(A\mid B^c)=0.95 and both inputs have probability 1/2, so

\mathbb{P}(B\mid A)=\frac{0.01\times 1/2}{0.01\times 1/2+0.95\times 1/2}=\frac{0.01}{0.96}=\frac{1}{96}.