Respuesta :
Answer:
[tex]P(X\leq 3) = P(X=1) +P(X=2) +P(X=3)[/tex]
[tex]P(X=1) = (1-0.6)^{3-1} 0.6 = 0.096[/tex]
[tex]P(X=2) = (1-0.6)^{3-2} 0.6 = 0.24[/tex]
[tex]P(X=3) = (1-0.6)^{3-3} 0.6 = 0.60[/tex]
[tex]P(X\leq 3) = 0.096 +0.24 +0.60= 0.936[/tex]
Step-by-step explanation:
Assuming the following info for the scenario 6-16: "Scenario 6-16
A poll shows that 60% of the adults in a large town are registered Democrats. A newspaper reporter wants to interview a local democrat regarding a recent decision by the City Council. "
Previous concepts
The geometric distribution "represents the number of failures before you get a success in a series of Bernoulli trials". And the density function is given by:
[tex] P(X) = (1-p) ^{x-1} p[/tex]
Where [tex] X \geq 1[/tex]
what is the probability that he will find a Democrat by the time he has stopped three people?
For this case we can assum that the random variable X represent the number of people selected in order to find a democrat and for this case we can assume that our random variable follows a geometric distribution.
[tex] X \sim Geome (p=0.60)[/tex]
We can find a democrat selecting 1, 2 or 3 people so we need to find this probability.
And for this case we want this probability:
[tex]P(X\leq 3) = P(X=1) +P(X=2) +P(X=3)[/tex]
[tex]P(X=1) = (1-0.6)^{3-1} 0.6 = 0.096[/tex]
[tex]P(X=2) = (1-0.6)^{3-2} 0.6 = 0.24[/tex]
[tex]P(X=3) = (1-0.6)^{3-3} 0.6 = 0.60[/tex]
[tex]P(X\leq 3) = 0.096 +0.24 +0.60= 0.936[/tex]
