Question

Probability question!

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement.

A: {One of the balls is yellow}
B: {At least one ball is red}
C: {Both balls are green}
D: {Both balls are of the same color}

Find:
P(A|B-compliment)
P(A-overline|B)

Answer 1

\[P(1\ yellow)=\]
\[P(1\ yellow)=\frac{\left(\begin{matrix}1 \\ 1\end{matrix}\right)\left(\begin{matrix}5 \\ 1\end{matrix}\right)}{\left(\begin{matrix}6 \\ 2\end{matrix}\right)}=\frac{5}{15}\]

Answer 2

\[P(1\ red)=\frac{2C1\times 4C1}{6C2}=you\ can\ calculate?\]
\[P(2\ red)=\frac{2C2\times 4C0}{6C2}=you\ can\ calculate?\]
\[P(at\ least\ 1\ red)=P(1\ red)+P(2\ red)\]

Answer 3

but 5/15 is not the answer :(

Answer 4

But the answer to A must be simplified as follows giving two possible forms of the answer:
\[\frac{3}{15}=\frac{1}{3}\]
Or alternatively
\[\frac{3}{15}=0.3333\]

Answer 5

ohh!! that makes sense now! thanks!

Answer 6

You're welcome :)