A radio station runs a promotion at an auto show with a money box with $13 \$ 100$ tickets, $15 \$ 50$ tickets, and $13 \$ 25$ tickets. The box contains an additional 20 "dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that all three tickets have no value.
The probability that all three tickets drawn have no money value is $\square$.
(Round to four decimal places as needed.)
Answer
\(\boxed{0.000056}\) is the probability that all three tickets drawn have no money value, or 0.0056% when expressed as a percentage.
Step 1 ：Calculate the total number of tickets in the box: \(13 \times 100 + 15 \times 50 + 13 \times 25 + 20 = 1300 + 750 + 325 + 20 = 2395\) tickets.
Step 2 ：Identify the number of 'dummy' tickets: 20 tickets.
Step 3 ：Calculate the probability of drawing the first 'dummy' ticket: \(\frac{20}{2395}\).
Step 4 ：Calculate the probability of drawing the second 'dummy' ticket, after one has already been drawn: \(\frac{19}{2394}\).
Step 5 ：Calculate the probability of drawing the third 'dummy' ticket, after two have already been drawn: \(\frac{18}{2393}\).
Step 6 ：Calculate the total probability that all three tickets drawn have no money value: \(\frac{20}{2395} \times \frac{19}{2394} \times \frac{18}{2393}\).
Step 7 ：\(\boxed{0.000056}\) is the probability that all three tickets drawn have no money value, or 0.0056% when expressed as a percentage.
