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.
To find the probability that at least two out of the three students plan on attending college, we need to calculate the probability of exactly two students planning on attending college and the probability of all three students planning on attending college.
The probability of exactly two students planning on attending college can be calculated using the combination formula:
C(3, 2) = 3
P(exactly 2 students) = 3 * (0.82)^2 * (0.18)^1 = 0.4601
The probability of all three students planning on attending college is:
P(all 3 students) = (0.82)^3 = 0.5514
Therefore, the probability of at least two out of the three students planning on attending college is the sum of the two probabilities:
P(at least 2 students) = P(exactly 2 students) + P(all 3 students)
P(at least 2 students) = 0.4601 + 0.5514 = 1.0115
Rounded to the nearest percent, the probability is 101%.