Question

A survey of high school juniors found that 78% of students plan on attending college. If you pick three students at random, what is the probability that at least two plan on attending college? Round to the nearest percent.
a) 53%
b) 12%
c) 40%
d) 88%

Answer 1

Please help!

Answer 2

Well, for any 1 student you might select, what is the probability that they plan to attend college?

Answer 3

50/50?

Answer 4

How do you get that?

Answer 5

well, there's only two choices and either one is a possibility.

Answer 6

"at least two" means
not none,
not one

compute \(P(x=0)\) and \(P(x=1)\) and subtract the result from 1

Answer 7

oh i see, there are only three students
so you could also compute \(P(x=2)\) and \(P(x=3)\) and add them

Answer 8

binomial distribution
\[P(x=2)=3\times (.78)^2\times (.22)\] and
\[P(x=3)=(.78)^3\] if it is not clear where these numbers come from, let me know

Answer 9

No, I understand. This is how I solved the equation but I got it wrong some how...

\[3C2 (.78)^2 * (.22)^1\]

Answer 10

Should I not have the 1 above .22?

Answer 11

that is \(P(x=2)\) yes
and \(_3C_2=3\)

Answer 12

did you add \((.78)^3\) to your result?

Answer 13

No.

Answer 14

it says "at least two" so it means "two or three"
you have to add them

Answer 15

ah ok

Answer 16

So the answer's d-) 88% right?

Answer 17

@satellite73 ?

Answer 18

i don't know, i didn't compute it
hold on i will check

Answer 19

Thanks :)

Answer 20

I get 0.876096 for that result..so yeah.

Answer 21

http://www.wolframalpha.com/input/?i=3*%28.78%29^2*.22%2B.78^3

Answer 22

I did too I just rounded. :)

Answer 23

yeah, looks good

Answer 24

Thanks so much for the help!