Suppose that a large university contains 10 percent mountain climbers. if four students are randomly sampled from the university, find the probability that at least one student is a mountain climber. g

The probability to find at least one climber is the complement of the probability of finding none:
P(k ≥ 1) = 1 - P(k = 0)

In order to find P(k = 0) you need to use the binomial distribution:
[tex]P(k) = \frac{n!}{k!(n-k)!} p^{k}(1 - p)^{n-k} [/tex]
where:
n = total number of events
k = number of events we want successful
p = probability of success

Therefore:
[tex]P(k=0) = \frac{4!}{0!(4-0)!} 0.1^{0}(1 - 0.1)^{4-0} [/tex]
=  (1 - 0.1)⁴
= 0.6561

Now you can calculate:
P(k ≥ 1) = 1 - P(k = 0) 
             = 1 - 0.6561
             = 0.3439

Hence, the probability of finding at least one climber if four students are randomly sampled is 34.39%.