A computer receives input over a faulty connection. For a particular transmissio

Question

A computer receives input over a faulty connection. For a particular transmission, 70% of the bits sent consists of 0’s; the rest are 1’s. You can assume that each bit of data is independent of each other bit. The 0’s have a 90% chance of being received correctly; the 1’s have a 92% chance of being received correctly. Anything which is not received correctly is received as the other number.

a) Overall, what percent of the data is received as a 1?

b) What is the chance that a 0 is received OR a 1 is sent?

c) For a given set of 10 bits, what is the chance that exactly 3 bits sent are 1’s?

d) Given that a 1 is received, what is the chance that a 1 was sent?

I just want to know d) solution

Explanation / Answer

d)

Let
Z = a 0 was sent
z = a 0 was received
I = a 1 was sent
i = a 1 was received

Here,

As

P(i) = P(I) P(i|I) + P(Z) P(i|Z) = (1-0.70)*0.92 + 0.70*(1-0.90) = 0.346

Therefore,

P(I|i) = P(I) P(i|I)/P(i) = (1-0.70)*0.92/0.346 = 0.797687861 [ANSWER]

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