Question

In Southern Ontario, a growing number of persons pursuing a teaching credential are choosing paid
internships over traditional student teaching programs. A groups of 8 candidates for three local
teaching positions consisted of five candidates who had enrolled in paid internships and three
candidates who had enrolled in traditional student teaching programs. Let us assume that all eight
candidates are equally qualified for the positions. Let X represents the number of internship‐trained
candidates who are hired for these three positions.

Answer 1

a) Find the probability that three internship‐trained candidates are hired for these positions.
b) What is the probability that none of the three hired was internship‐trained?
c) Find P(X ≤ 1).

Answer 2

@tkhunny @phi @satellite73 @mathslover please help.....any help is good

Answer 3

Please don't tag the world. We're here or we aren't. We'll see it.

You DO need to show your work. Let's see your efforts.

Answer 4

sorry

Answer 5

So, we're randomly picking 3 from 8 and the question is, what is the probability that all 3 selected are internship-trained. Does that sound like a proper understanding of the question?

Answer 6

i was gonna use the binomial prob distribution equation, but i don't have p. Would I just use this equation instead \[c =\frac{ n! }{ r!(n-r)!}\]

Answer 7

How about: \(P(0) = \dfrac{\left(\begin{matrix}0 \\ 3\end{matrix}\right)\left(\begin{matrix}3 \\ 5\end{matrix}\right)}{\left(\begin{matrix}3 \\ 8\end{matrix}\right)}\)

\(P(1) = \dfrac{\left(\begin{matrix}1 \\ 3\end{matrix}\right)\left(\begin{matrix}2 \\ 5\end{matrix}\right)}{\left(\begin{matrix}3 \\ 8\end{matrix}\right)}\)

\(P(2) = \dfrac{\left(\begin{matrix}2 \\ 3\end{matrix}\right)\left(\begin{matrix}1 \\ 5\end{matrix}\right)}{\left(\begin{matrix}3 \\ 8\end{matrix}\right)}\)

\(P(3) = \dfrac{\left(\begin{matrix}3 \\ 3\end{matrix}\right)\left(\begin{matrix}0 \\ 5\end{matrix}\right)}{\left(\begin{matrix}3 \\ 8\end{matrix}\right)}\)

Answer 8

ummm just a little question, what does it mean when you have this ( ) with the numbers inside.....i have never seen those before

Answer 9

Same as \(C(n,r) = \left(\begin{matrix}n \\ r\end{matrix}\right) = \dfrac{n!}{r!(n-r)!} = \;^{n}C_{r} =\;_{n}C_{r}\)

Answer 10

Different notations develop for different reasons. You just have to keep your eyes on the all!

Answer 11

ohh....i use a different notation. Could you explain why you set up the equations like that? You multiple then divide to get the probability, i dont understand why.

Answer 12

For P(3) we have to do three things:

1) Pick all three from among the three internship candidates
2) Pick none from the 5 other candidates
3) Pick 3 from among all 8 candidates.

Each of those has its own piece of the formulation.

Note how the third part is the same in all four calculations.

Answer 13

Oh, so for each probability you are either picking 0 from the other candidates and 3 from the internship. This is for P(3)

Answer 14

so for b it will be the p(0) and for c it will be p(0) + p(1)

Answer 15

That's right.

Answer 16

thank you! and sorry at the same time

Answer 17

No worries. It's why we're here. Not much more rewarding than helping people who want to work and are willing to show their efforts.