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.

Question

(1 point)
A) 91%

B) 9%

C) 45%

D) 36%

Answer 1

To calculate the probability that at least two students plan on attending college, we can first calculate the probability that exactly two students plan on attending college and add that to the probability that all three students plan on attending college.

The probability that exactly two students plan on attending college is calculated as:
P(2 students plan on attending college) = (0.82)^2 * (0.18) = 0.1361

The probability that all three students plan on attending college is calculated as:
P(3 students plan on attending college) = (0.82)^3 = 0.5514

So, the probability that at least two students plan on attending college is:
P(at least 2 students plan on attending college) = P(2 students plan on attending college) + P(3 students plan on attending college) = 0.1361 + 0.5514 = 0.6875

Converting this to a percentage and rounding to the nearest percent, we get 69%. Therefore, the answer is not provided among the answer choices.