Question

In a bag there are 40 blocks, 16 red and 24 yellow. A contestant blindly reaches in the bag and grabs a predetermined number of blocks. If the contestant grabs 13 blocks, what is the probability more than 10 of them are red?

Answer 1

\[P(11\ red)=\frac{\left(\begin{matrix}16 \\ 11\end{matrix}\right)\left(\begin{matrix}24 \\ 2\end{matrix}\right)}{\left(\begin{matrix}40 \\ 13\end{matrix}\right)}\ .....(1)\]
\[P(12\ red)=\frac{\left(\begin{matrix}16 \\ 12\end{matrix}\right)\left(\begin{matrix}24 \\ 1\end{matrix}\right)}{\left(\begin{matrix}40 \\ 13\end{matrix}\right)}\ .......(2)\]
\[P(13\ red)=\frac{\left(\begin{matrix}16 \\ 13\end{matrix}\right)}{\left(\begin{matrix}40 \\ 13\end{matrix}\right)}\ ......(3)\]
The probability that more than 10 are red is found by adding the values of probability found in (1), (2) and (3).