Probability
Example 4: using the probability rules
It is known that the probability that a child will buy a phantom comic is \(0.3\). If \(3\) children purchase comics at the same time, what is the probability that:
a) all will purchase a phantom comic?
b) none will purchase a phantom comic?
c) only one child will purchase a phantom comic?
Solution:
Let \(A\) represent a child will purchase a Phantom comic.
a) \begin{eqnarray*}
P(\mbox{All purchase}) &=& P(A) \times P(A) \times P(A) \\
&=& 0.3 \times 0.3 \times 0.3 \\
&=& 0.027
\end{eqnarray*}
b) \begin{eqnarray*}
P(\mbox{none purchase}) &=& P(\bar{A})\times P(\bar{A})\times P(\bar{A}) \\
&=& 0.7 \times 0.7 \times 0.7 \\
&=& 0.343
\end{eqnarray*}
c) \begin{eqnarray*}
&& P(\mbox{1 purchase}) \\
&=& P(A\,,\ \bar{A}\,,\ \bar{A}) + P(\bar{A}\,,\ {A}\,,\ \bar{A}) + P(\bar{A}\,,\ \bar{A}\,,\ {A}) \\
&=& 0.3\times 0.7 \times 0.7 + 0.7 \times 0.3\times 0.7 + 0.7\times0.7\times0.3 \\
&=& 3 \times (0.3\times0.7\times0.7) \\
&=& 0.441
\end{eqnarray*}