In a class of 30 students, a student can be classified as junior or senior, and a member of one of the three competitive teams: red, blue, and green teams.

Question

(a) How many possible outcomes are there in the experiment?

(b) What is the probability that at least one of the students is a junior student?

(c) What is the probability that no student is a member of the green team?

Answer 1

a) As each student can be a junior or a senior, and red, blue, or green, there are 6 possible outcomes for each student. There are 30 students, so there are 6^30 possible outcomes.

b) The probability is 1/2 that each student is male. Then, the probability of at least 1 junior = 1 - the probability of all seniors = 1 - (1/2)^30 or 1 - 1/2^30 = 1073741823/1073741824 is approximately .999999999

c) The probability of a student being green, as there are 3 colors, is 1/3, so the probability of not being green is 2/3

Then, the probability of all 30 students being not green is (2/3)^30 =2^30/3^30 = 1073741824/205891132094649 , which is approximately 5.2151 * 10^-06