weary of the low turnout in elections, administration decides to choose an srs of three students to form an advisory board that represents student opinion. suppose that 40% of all students oppose the use of federal fund to support student interest groups and that the opinions of the three students on the board are independent. then the probability is 0.4 that each opposes the funding of interest groups. let x be the number of student representatives who oppose the funding of interest groups. what is the probability of a majority of the advisory board opposes to funding?

Two events are said to be independent of each other if the probability that one event occurs in no way affects the probability of the other event occurring .If A and B are independent events then the probability that they all occur is given by P(A) x P(B)

Here, the opinions of the three students on the board are independent the probability is 0.4 that each opposes the funding of interest groups

Mjority of the board opposes can be when two or more members oppose it.

P(ABC) = P(A) x P(B) x P(C)

P(ABC) = 3 (0.6) x 0.4 x 0.4 + 0.4 x 0.4 x 0.4

= 0.288 + 0.064

= 0.352

Therefore, the probability of a majority of the advisory board opposes to funding is 0.352

To learn more about probability refer here

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