Question

A survey of high school juniors found the 75% of the students plan on attending college. If you pick 3 students at random, what is the probability that at least two plan on attending college? Round to the nearest percentage.

Answer 1

Assuming you pick 3 students at random, The probability that at least two plan on attending college is 84%.

Probability

Using Binomial Distribution

Given:

n = 3

p = 0.75

q = 1-0.95 = 0.25

Hence:

P[≥2] = P[2] + P[3]=(3c2 ×0.75²×0.25) + 0.75³

P[≥2] = P[2] + P[3]=0.421875+0.421875

P[≥2] = P[2] + P[3]=0.84375×100

P[≥2] = P[2] + P[3]=84% (Approximately)

Inconclusion the probability that at least two plan on attending college is 84%.

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