Answer to Question #91523 in MathCAD for matimu

Question #91523
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?
1
Expert's answer
2019-07-09T02:18:26-0400

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)=n!k!(nk)!pk(1p)nkP(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(k2)=P(0)+P(1)+P(2)P(k\le2)=P(0)+P(1)+P(2)


Answer: 83.69%


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