Based on a​ poll, among adults who regret getting​ tattoos, 19 percent say that they were too young when they got their tattoos. Assume that seven adults who regret getting tattoos are randomly​ selected, and find the indicated probability.Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos

This problem can be modeled as a binomial probability problem, where we are calculating the probability of exactly one success (i.e., one adult saying they were too young to get tattoos) out of a total of seven trials (adults selected).

The formula for the binomial probability is:

\[
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}
\]

Where:
- \( P(X = k) \) is the probability of getting exactly \( k \) successes,
- \( n \) is the total number of trials (adults),
- \( k \) is the number of successes (people saying they were too young),
- \( p \) is the probability of success on a single trial,
- \( \binom{n}{k} \) is the binomial coefficient, which is calculated as \( \frac{n!}{k!(n - k)!} \).

### Given:
- \( n = 7 \) (7 adults),
- \( k = 1 \) (exactly 1 adult saying they were too young),
- \( p = 0.19 \) (19% of adults who regret getting tattoos say they were too young).

We can now calculate the probability \( P(X = 1) \):

\[
P(X = 1) = \binom{7}{1} \cdot (0.19)^1 \cdot (1 - 0.19)^{7 - 1}
\]

Let's compute this.The probability that exactly one of the selected seven adults says they were too young to get tattoos is approximately \( 0.376 \), or 37.6%.

Would you like more details on this calculation or have any questions?

Here are 5 related questions to explore this topic further:
1. What is the probability that none of the selected adults say they were too young to get tattoos?
2. What is the probability that exactly two of the selected adults say they were too young?
3. How would the probability change if we selected 10 adults instead of 7?
4. What is the expected number of adults who regret getting tattoos because they were too young out of 7?
5. How does increasing the probability \( p \) to 0.25 affect the probability of one adult saying they were too young?

**Tip:** Binomial probabilities are useful when you have independent trials with two outcomes, such as success/failure.

Based on a poll, among adults who regret getting tattoos, 19 percent say that they were too young when they got their tattoos. Assume that seven adults who regret getting tattoos are randomly selected, and find the indicated probability. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

Explore how to calculate the probability that exactly one out of seven selected adults regrets getting a tattoo because they were too young, using binomial probability. This problem involves core concepts of probability theory and combinatorics, ideal for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation