The problem states that every 30th person in line gets a coupon, meaning that 1 out of every 30 people will receive a coupon.

Step 1: Calculate the probability of getting a coupon.

Since every 30th person gets a coupon, the probability of getting a coupon is: $P(\text{getting a coupon}) = \frac{1}{30}$

Step 2: Calculate the probability of not getting a coupon.

The probability of not getting a coupon is the complement of the probability of getting one, which is: $P(\text{not getting a coupon}) = 1 - \frac{1}{30} = \frac{29}{30}$

Thus, the probability that you don’t get a coupon is: $P(\text{not getting a coupon}) = \frac{29}{30}$

Final Answer:

The probability that you don’t get a coupon is: $\frac{29}{30} \approx 0.9667$ If you want to round it to four decimal places, it is: $0.9667$

Would you like more details or have any other questions?

Here are five related questions:

1. What is the probability of getting a coupon if you're in a line of 90 people?
2. If 300 people are in line, how many would you expect to get a coupon?
3. What is the probability of getting a coupon if you stand in line twice?
4. How does the probability change if every 20th person gets a coupon instead?
5. What is the probability of not getting a coupon if you stand in line 3 times?

Tip: When calculating complementary probabilities, remember that they are always $1 - P(\text{event})$.