Suppose we transmit 16 information bits through a digital communication system w

Question

Suppose we transmit 16 information bits through a digital communication system which has the property that the probability of a bit value being received correctly is 0.995. Obviously then, the probability of a particular bit being incorrectly transmitted is then 0.005. Whether a particular bit is transmitted correctly has nothing to do with whether any other bit is correctly transmitted. (a) Find the probability that all 16 bit values are correctly received. (b) In another communications system, the situation is the same except that the probability of a bit error drops to 10-6. Find the probability that 16 bits transmitted through this system are all received correctly. Find as well the probability that one million bits sent through this better system all were received correctly. Values for these answers are required, not merely expressions

Explanation / Answer

a. Probability that a single bit is transmitted correctly = 0.995

Pr( All 16 bit values are correctly received ) = 0.99516 = 0.9229

b. Probability that a single bit is transmitted correctly = 1 - 10-6 = 0.999999

Pr( All 16 bit values are correctly received ) = 0.99999916 = 0.999984

Pr( 1 million bits are correctly received ) = 0.9999991000000 = 0.367879

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