Question

A survey of high school juniors found that 82% 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?
I know the equation is:
nCx(p)^x(q)^n-x
but i cant remember what variable means what..

Answer 1

You have to assume that because the population is large and the sample is small, the distribution is binomial, i.e. the probability is always 0.82.
So the probability that a student is NOT planning to attend college is 1-0.82=0.18.

Suppose X is the number of students in the sample that are planning to attend, the X is binomially distributed, with p=0.82 and n=3.

We have to find \(P(X \geq 2)=P(X=2)+P(X=3)\).
\[P(X=2)=\left(\begin{matrix}3 \\ 2\end{matrix}\right) (0.82)^2\cdot (0.18)^1\]\[P(X=3)=\left(\begin{matrix}3 \\ 3\end{matrix}\right) (0.82)^3\cdot (0.18)^0\]So\[P(X=2)=3 \cdot (0.82)^2\cdot 0.18 \approx 0.363096\]\[P(X=3)=1 \cdot (0.82)^3 \cdot 1 \approx 0.551368\]

Answer 2

So \(P(X \geq 2) \approx 0.363096+0.551368 = 0.914464\)

Answer 3

THANK YOU SO MUCH!!

Answer 4

Welcome!