Respuesta :
Answer:
0.034 = 3.4% probability that they all are fans of professional baseball.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they are fans of professional baseball, or they are not. The probability of a person being fan of professional baseball is independent of any other person. So we use the binomial probability distribution to solve this question.
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.
43% of Americans are fans of professional baseball.
This means that [tex]p = 0.43[/tex]
If 4 people are selected at random, find the probability that they all are fans of professional baseball.
This is P(X = 4) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.43)^{4}.(0.57)^{0} = 0.034[/tex]
0.034 = 3.4% probability that they all are fans of professional baseball.
