Question

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. 71.9% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick seven first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status. What is the probability that at least two of the freshmen reply "yes"? (Round your answer to four decimal places.)

Answer 1

Let the number of freshman that reply "yes" for having the right to legal marital status be X.

The given problem can be solved with the help of binomial distribution as the probability of success for the random variable and the sample size is given.

Here, n = 7 (i.e Number of randomly picked full time freshman)

p = 71.9% = 0.719 (I.e Probability that student reply "yes")

Thus, q = 1 - p = 0.281

Now, To find the probability that atleast two of the freshman reply "yes"

i.e P( X >= 2 ) = 1 - P(X < 2) = 1 - { P(X = 0) + P(X = 1)}

= 1 - {}

= 1 - 0.002616

= 0.9974

Thus, the required probability is 0.9974