A space probe is controlled by 7 different instructions from the ground. the probabilities of sending these instructions vary - the three most common instructions have probabilities 1/2, 1/4, and 1/8 of being sent, respectively. the remaining four instructions are equally likely to be sent. in expectation, what is the minimum number of whole number bits required to communicate with the probe?

Question

Mathematics

Karli

8 July, 06:18

A space probe is controlled by 7 different instructions from the ground. the probabilities of sending these instructions vary - the three most common instructions have probabilities 1/2, 1/4, and 1/8 of being sent, respectively. the remaining four instructions are equally likely to be sent. in expectation, what is the minimum number of whole number bits required to communicate with the probe?

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Russell · Answer 1

The space probe needs to be able to differentiate 7 different type of command.

The possible way that can be code by n bits would be 2^n. Then, the number of bits for coding at least 7 different commands would be:

2^n > 7

2^n > 2^2.80

n > 2.80

n=3

You need at least 3 bits