Question

3. A magnetic tape storing information in binary form has been corrupted, so it can only be read with bit errors. The probability that you correctly detect a 0 is 0.9, while the probability that you correctly detect a 1 is 0.85. Each digit is a 1 or a 0 with equal

Answer 1

Answer:

3.

Given,

To determine the required probability

Let X be the event of getting a bit 0 or 1

i.e.,

P(X) = P(0) = P(1) = 1/2

Let us assume that Y be the event of effectively recognizing the number

It is given that ,

P(Y|0) = 0.9

P(Y|1) = 0.85

P($\bar{y}$|0) = 0.1

P($\bar{y}$|1) = 0.15

Given that you read a 1, probability that this is a correct reading

i.e.,

P(1|Y) = P(1)*P(Y|1) / (P(1)*P(Y|1) + P(0)*P($\bar{y}$|0) )

substitute the given values in above expression

P(1|Y) = 1/2 * 0.85 / (1/2*0.85 + 1/2*0.1)

= 0.425 / (0.425 + 0.05)

= 0.425 / 0.475

= 0.8947

Required probability = 0.8947