Question

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?

Answer 1

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