O lvl E Maths: Probability

From http://www.sgforums.com/forums/2297/topics/348803

Suppose that 45% and 40% of Singaporeans approve and disapprove the idea of building a casino respectively. If three Singaporeans are interviewed at random,find the probability that
a) all of them will either approve or disapprove of the idea

b) at least two of them will not approve of the idea

c) at most one of them will approve of the idea.

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Answer:

Let A = Approve, D = disapprove

(a) P(all of them have opinions) = 0.85 * 0.85 * 0.85 = 4913/8000

(b) Let X = not disapprove
P(X) = 1 - 0.4 = 0.6

P(at least 2 disapprove) = P(DDX) + P(DXD) + P(XDD) + P(DDD)
= 3 (0.4 * 0.4 * 0.6) + 0.4 * 0.4 * 0.4
=44/125

(c) Let NA = not approve
P(NA) = 1 - 0.45 = 0.55

P(at most 1 approve) = P(all NA) + 3 P(A.NA.NA)
= 0.55 * 0.55 * 0.55 + 3 (0.45 * 0.55 * 0.55)
= 2299/4000

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