Given that every thirtieth person in line will get a coupon for a free box of popcorn at the movies, what is the probability that you don’t get a coupon when you’re in line? Enter a fraction or round your answer to 4
 decimal places, if necessary

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 \( 1 - P(\text{event}) \).

Given that every thirtieth person in line will get a coupon for a free box of popcorn at the movies, what is the probability that you don’t get a coupon when you’re in line? Enter a fraction or round your answer to 4 decimal places, if necessary.

Learn how to calculate the probability of not getting a coupon when every 30th person in line receives one. This problem explores key probability concepts such as complementary events and the complement rule in probability. The solution includes step-by-step calculations with final answers in both fraction and decimal forms, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation