A high school guidance counselor conducts a survey to find the student's first choice for a college major and found that 65% of students choose math. If three students are chosen at a random, what is the probability that at least one of them would choose math?

prob(choose math) = .65

prob(not to choose math) = .35

prob(at least 1 of 3 choosing math)
= 1 - prob(nobody choosing math)
= 1 - C(3,0) (.35)^3
= 1 - .042875
= appr .957

or

prob(1 choosing math) + prob(2 choosing math) + prob(3 choosing math)
= .957

To find the probability that at least one of the three students would choose math, we can use the concept of complementary events.

First, let's find the probability that none of the three students choose math. Since 65% of students choose math, the probability that a student does not choose math would be 100% - 65% = 35%.

To find the probability that all three students chosen do not choose math, we multiply the probabilities together:

P(None choose math) = 35% * 35% * 35% = 0.35 * 0.35 * 0.35 = 0.0429.

Now, to find the probability that at least one of the three students chooses math, we subtract the probability that none of the students chooses math from 1:

P(At least one chooses math) = 1 - P(None choose math) = 1 - 0.0429 = 0.9571.

Therefore, the probability that at least one of the three students would choose math is approximately 0.9571 or 95.71%.

To summarize, the probability can be calculated by finding the complementary event (probability that none of the students choose math) and subtracting it from 1.