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

Step-by-step 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 = $\dfrac{1}{2}=0.5$

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 :-

$P(x\geq1)=1-P(z$

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