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A magnetic tape storing information in binary form has been corrupted, so it can only be readwith bit errors. The probability that you correctly detect a 0 is 0.9, while the probability thatyou correctly detect a 1 is 0.85. Each digit is a 1 or a 0 with equal probability. Given that youread a 0, what is the probability that this is a correct reading?

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sqdancefan

Answer:

  6/7 ≈ 85.7%

Step-by-step explanation:

The probability that a 0 was transmitted and received is 0.5·0.9 = 0.45.

The probability that a 1 was transmitted and a 0 received is 0.5·0.15 = 0.075.

Then the probability that a 0 was received is 0.45 +0.075 = 0.525.

The probability of interest is ...

  p(0 transmitted | 0 received) = p(0 transmitted & received)/p(0 received)

  = 0.45/0.525 = 6/7 ≈ 85.7%

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