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 = [tex]\dfrac{1}{2}=0.5[/tex]
Binomial probability distribution formula :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], 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 :-
[tex]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[/tex]
Hence, the probability that you picked a string with at least one zero = 0.9990
