Answer
$\frac{85}{58570512}$
Work Step by Step
Step 1. Choose 5 numbers from $1\ to\ 56$. We have $_{56}C_5$ combinations.
Step 2. Choose 1 number from $1\ to\ 46$. We have 46 choices.
Step 3. The total sample space is $46\times_{56}C_5$
Step 4. To win the prize, we need to match 4 numbers out of 5 or $_{5}C_4$, leaving one in $51$ (non-winning balls). Thus the total ways for this part is
$51\times_{5}C_4$
Step 5. There is only one way to select the gold ball. Thus the total ways of winning is
$51\times_{5}C_4=255$
Step 6. The probability of winning this prize is
$p=\frac{255}{46\times_{56}C_5}=\frac{255}{46(3819816)}=\frac{85}{58570512}$
