Respuesta :
Answer:
Probability that at least one of them suffers from arachnophobia is 0.5160.
Step-by-step explanation:
We are given that a 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders (arachnophobia).
Also, At a summer camp there are 10 teenagers sleeping in each tent.
Firstly, the binomial probability is given by;
[tex]P(X=r) =\binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....[/tex]
where, n = number of trials(teenagers) taken = 10
r = number of successes = at least one
p = probability of success and success in our question is % of
the teenagers suffering from arachnophobia, i.e. 7%.
Let X = Number of teenagers suffering from arachnophobia
So, X ~ [tex]Binom(n= 10,p=0.07)[/tex]
So, probability that at least one of them suffers from arachnophobia
= P(X >= 1) = 1 - probability that none of them suffers from arachnophobia
= 1 - P(X = 0) = 1 - [tex]\binom{10}{0}0.07^{0}(1-0.07)^{10-0}[/tex]
= 1 - (1 * 1 * [tex]0.93^{10}[/tex] ) = 1 - 0.484 = 0.5160 .
Therefore, Probability that at least one of them suffers from arachnophobia is 0.5160 .
