A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?
5.1%
10%
27%
15%

Question

A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative? 
5.1%
10%
27%
15%

anonymous · Answer

@campbell_st @Luis_Rivera  @robtobey @phi Someone please explain how I get the answer, thanks!

campbell_st · Answer

this is a binomial probability question. 

which uses 

$$P( n..successes ..and.. n-k..failures ..\in..any..order) =  ^nC_{k}  p^kq^{n - k}$$

so in your question n = 10 and k = 5

p = 0.76 and q = 0.24


so you are evaluating 

P(5 in favour) = $$^{10}C_{5}(0.76)^5 \times (0.24)^{10-5}$$

hope this helps.

anonymous · Answer

What would I do next? Sorry, I'm really bad at this probability math :/ @campbell_st

campbell_st · Answer

well all you need to do is evaluate the combination 

$$^{10}C_{5} = = \frac{10!}{5!(10 - 5)!} = 252$$

so you need to evaluate 

P(5 in favour) = $$252\times (0.76)^5\times (0.24)^5$$

that will give an answer as a decimal, so multiply by 100 to get the percentage.

anonymous · Answer

Sweet, thanks so much for the help:)