A poll is given, showing 35% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

Question

Karter

Mathematics

18 July, 08:46

A poll is given, showing 35% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

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Kelsie Garner · Answer 1

18.7%

Step-by-step explanation:

This is a case of binomial distribution. The formula is as follows:

P = 8C4 * (p ^ x) * [ (1-p) ^ (n-x) ]

Now, we have to p = 0.35, n = 8 and x = 4.

8C4, means combinations of 8 in 4, the combination formula is:

nCx = n! / [x! * (n-x) !]

Replacing

8C4 = 8! / [4! * (8-4) !] = 8! / (4! * 4!) = 70

Now we can replace all values in the main formula:

P = 70 * (0.35 ^ 4) * [ (1-0.35) ] ^ (8-4)

P = 70 * (0.35 ^ 4) * (0.65 ^ 4) = 0.187

Therefore, there is an 18.7% is the probability that exactly 4 of them favor the new building project