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, wht is the probability that exactly five of them will vote in favor of the initiative?

Answer 1

binomial for this one

Answer 2

5 will be in favor , 5 will not
\[P(X=5)=\binom{10}{5}(.76)^5\times (.24)^5\] and a calculator

Answer 3

or wolfram
http://www.wolframalpha.com/input/?i=P%28X%3D5%29%3D \binom{10}{5}%28.76%29^5\times+%28.24%29^5

Answer 4

im lost.....

Answer 5

okay lets go slow

Answer 6

ok

Answer 7

"a poll shows that 76% of voters in a city favor an initiative " says
the probability that a person is in favor of the initiative is \(.76\)

Answer 8

and therefore the probability they are not is \(1-.76=.24\)
is that part okay?

Answer 9

yes

Answer 10

ok good, now do you know how to compute a "binomial" probability? i am guessing "no"

Answer 11

no

Answer 12

you have 10 people all together
you want to know the probability that exactly 5 are in favor, which of course means the other five are not

Answer 13

ok

Answer 14

you multiply all the probabilities together
that is, you take \((.76)^5\) and multiply it by \((.26)^5\) that is for the five that are in favor, and the five that are not

Answer 15

3.01

Answer 16

that would be something like having the first 5 in favor, and the second 5 not in favor
they would vote
(yes, yes, yes, yes, yes, no, no, no , no , no)

Answer 17

but there are other possible arrangement of this, for example
(yes, no, yes, yes, no, yes, no, no , no , no, yes)

Answer 18

the question is "how many" and that is the same as asking 'out of 10 people, how many ways are there to choose 5?" which is sometimes written as \(\binom{10}{5}\)
and sometimes written as \(_{10}C_5\)
have you seen either of these?

Answer 19

the second one

Answer 20

okay then we will use that

Answer 21

typo there,
your probability is therefore
\[_{10}C_5\times (.76)^5\times (.24)^5\]

Answer 22

ok but im not sure how to finish it with the first part.

Answer 23

you will need a calculator for this
\(_{10}C_5=525\) so on your calculator compute
\[252\times (.76)^5\times (.24)^5\]

Answer 24

sorry, i mean \(_{10}C_5=252\)

Answer 25

http://www.wolframalpha.com/input/?i=10+choose+5

Answer 26

ok if i take and times them i do not come up with any of the multiply choice answers

Answer 27

here is your "final answer"
http://www.wolframalpha.com/input/?i=%2810+choose+5%29+*%28.76%29^5*%28.24%29^5

Answer 28

answer as you can see is about \(.0509\)

Answer 29

would it be 5.1% then

Answer 30

as a percent, yes

Answer 31

i got it and thank you

Answer 32

yw