Answer
The probability of winning the prize is $0.0000004720$.
Work Step by Step
Consider the provided information.
We first calculate the total possible combinations of choosing the five numbers.
$\begin{align}
& _{50}{{C}_{5}}=\frac{50!}{\left( 50-5 \right)!5!} \\
& =\frac{50!}{45!5!} \\
& =\frac{\left( 50 \right)\left( 49 \right)\left( 48 \right)\left( 47 \right)\left( 46 \right)45!}{45!5!} \\
& =\frac{\left( 50 \right)\left( 49 \right)\left( 48 \right)\left( 47 \right)\left( 46 \right)}{5!}
\end{align}$
Further solve the above expression.
$\begin{align}
& _{50}{{C}_{5}}=\frac{\left( 50 \right)\left( 49 \right)\left( 48 \right)\left( 47 \right)\left( 46 \right)}{\left( 5 \right)\left( 4 \right)\left( 3 \right)\left( 2 \right)\left( 1 \right)} \\
& =\left( 10 \right)\left( 49 \right)\left( 4 \right)\left( 47 \right)\left( 23 \right) \\
& =2118760
\end{align}$
There can be just one outcome that can match the five numbers drawn randomly,
Thus,
$~\text{The probability of winning the prize}=\frac{\text{Number of outcomes in favour of win}}{\text{Total outcomes}}$
$~\text{The probability of winning the prize}=\frac{1}{2118760}\approx 0.0000004720$
Hence, the probability of winning the prize is $0.0000004720$
