A die is thrown 20 times. Use the bionomial distrubution to determine the probability of getting five successes in 20 trials, if rolling a 2 or a 4 is considered to be a success.
\(\displaystyle \[
\begin{}
p(5)\; = \;\left( \begin{}
N \hfill \\
k \hfill \\
\right)p^k (1 - p)^{N - k} \hfill \\
= \;\left( \begin{}
20 \hfill \\
5 \hfill \\
\right)\left( {\frac{1}
{3}} \right)^5 \left( {\frac{2}
{3}} \right)^{15} \hfill \\
= \;0.1457 \hfill \\
\]\)
The texaide doesn't seem to be working but the (Nk) should be NCk
Did I do this correctly?
\(\displaystyle \[
\begin{}
p(5)\; = \;\left( \begin{}
N \hfill \\
k \hfill \\
\right)p^k (1 - p)^{N - k} \hfill \\
= \;\left( \begin{}
20 \hfill \\
5 \hfill \\
\right)\left( {\frac{1}
{3}} \right)^5 \left( {\frac{2}
{3}} \right)^{15} \hfill \\
= \;0.1457 \hfill \\
\]\)
The texaide doesn't seem to be working but the (Nk) should be NCk
Did I do this correctly?
