Question

Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

What is the probability that you will need to ask fewer than three freshmen?

Short answer

The probability that less than three freshmen will need to be asked is $\mathbf{0}\mathbf{.}\mathbf{917}$.

Step-by-step solution

Given

Probability of success, $p=71.3\%=0.713$.

Concept used

We know that for a geometrical distribution,
$P(X=x)=p(1-p{)}^{1-x}$
where $x$ is that the number of freshmen asked and $p$is that the probability of success.

Calculation

We want to seek out the probability that but 3 freshmen will must be asked, i.e., $P(X<3)$.
$P(X<3)=P(X=1)+P(X=2)$

$=0.713+0.20463=0.917$