A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2. Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
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The probability of receiving a 0 given that a 0 was sent is 0.8. Since a 0 is sent two-thirds of the time, the overall probability of this event is 0.8 * 2/3 = 0.533. Show more…
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