Suppose that a satellite transmits data to Earth as a string of zeros and ones.

Question

Suppose that a satellite transmits data to Earth as a string of zeros and ones. Each bit (that is, each zero or one) has a probability p of being correctly transmitted from the satellite to the receiver on Earth. Further suppose that each bit is transmitted in triplicate (that is, instead of sending a message 1001, the satellite would send 111000000111), and the correct value for each bit taken to be the result shown by the majority of the triple representing the bit (that is, if 110 is received, we assume that a 1 was sent). What is the probability that a bit will be incorrectly interpreted?

Explanation / Answer

Fortheit to be incorrectly interpreted, there should be either 2 errors or 3 errors. So, P(bit will be incorrectly interpreted) = P(2 errors ) + P(3 errors)

= 3x p x (1-p)2 + (1-p)3

= (1-p)2 (3p + 1 - p)

= (1-p)2 (1+2p)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.