Question

the probability that a student is accepted to a prestigious college is 0.3. if 5 students from the same school apply,what is the probability that at most 2 are accepted?

Answer 1

The number of successes k in a series of n identical independent tests with the probability of success p in each trial has a binomial distribution. The probability function is given by the formula:

$$P(k)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}$$

The probability that at most 2 are accepted (n=5, p=0.3):

$$P(k\le2)=P(0)+P(1)+P(2)$$

Answer: 83.69%