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A 10 bit string is to be randomly picked from all possible 10 bit strings. What is the probability that you picked a string with at least one zero?

User Tobiah Rex
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1 Answer

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Answer: 0.9990

Explanation:

Given : The number of bits in a string = 10

The value taken by a bit is either 0 or 1.

Therefore, the probability that the bit is zero =
(1)/(2)=0.5

Binomial probability distribution formula :-


P(x)=^nC_xp^x(1-p)^(n-x), where P(x) is the probability of getting success in x trials , n is the total number of success and p is the probability of getting success in each trial.

Now, the probability that you picked a string with at least one zero is given by :-


P(x\geq1)=1-P(z<1)\\\\=1-P(0)\\\\=1-^(10)C_0(0.5)^(0)(0.5)^(10)\\\\=1-(0.5)^(10)=1-0.0009765625\\\\=0.9990234375\approx0.9990

Hence, the probability that you picked a string with at least one zero = 0.9990

User Jurek
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