A survey of high school juniors found that 82% of students plan on attending college. If you pick
three students at random, what is the probability that at least two plan on attending college?
Round to the nearest percent.
(1 point)
91%
9%
45%
36%
To calculate the probability that at least two out of three students plan on attending college, we need to calculate the probability of all three students planning on attending college (82% * 82% * 82%), the probability of two students planning on attending college and one not (82% * 82% * 18% * 3) since there are three ways in which this can happen, and finally the probability of only one student planning on attending college and the other two not (82% * 18% * 18%).
Adding these probabilities together, we get:
P(at least two students plan on attending college) = (82% * 82% * 82%) + (82% * 82% * 18% * 3) + (82% * 18% * 18%)
= (0.82 * 0.82 * 0.82) + (0.82 * 0.82 * 0.18 * 3) + (0.82 * 0.18 * 0.18)
= 0.5511 + 0.4291 + 0.0279
= 1.0081
Therefore, the probability is 101% which is not possible as probabilities cannot exceed 100%. Therefore, the closest option is to round down to 91%, as it is the closest option.
Therefore, the probability that at least two students plan on attending college out of three randomly chosen students is 91%.