Question

Please help me:
Six sophomores and 14 freshmen are competing for two alternate positions on the debate team.

Which expression represents the probability that both students chosen are sophomores?

Answer 1

http://www.probabilityformula.org/independent-events-probability.html

Answer 2

its option A

Answer 3

I'm not fully sure whether any of the three options given are correct, but maybe I'm just reading them wrong. If I understand the question correctly, we have:

A group of 20 people, 6S, 14F and we will be picking two of these.
We're looking for the probability that the two people picked for the debate team are S. So, the usual formula for this would be:

\[\frac{ (No.~ways~of~choosing~2~from~6)(No.~ways~of~choosing~0~from~14) }{ No.~ways~of~choosing~2~from~20 }\]

which we would represent as:
\[\frac{ \left(\begin{matrix}6 \\ 2\end{matrix}\right)\left(\begin{matrix}14 \\ 0\end{matrix}\right) }{ \left(\begin{matrix}20 \\ 2\end{matrix}\right) }\]

\[Here,~\left(\begin{matrix}6 \\ 2\end{matrix}\right)~means~'6~Choose~2'~and~so~on...\]

Answer 4

For option A which @anwaarullah mentioned, the denominator (bottom part of fraction) appears correct, but I don't understand where the top part comes from, given the numbers we are presented with in the question. That's why I felt it wasn't correct....

Answer 5

What do you think @abymartinez15 ?