Answer:
23.21% probability that out of six randomly selected called, exactly one will be dropped.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
5% of all cell phone calls are dropped.
This means that [tex]p = 0.05[/tex]
What is the probability that out of six randomly selected called, exactly one will be dropped?
This is [tex]P(X = 1)[/tex] when [tex]n = 6[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321[/tex]
23.21% probability that out of six randomly selected called, exactly one will be dropped.
