Based on a​ poll, among adults who regret getting​ tattoos, 12​% 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. Complete parts​ (a) through​ (d) below.
Question content area bottom
Part 1
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
  
enter your response here ​(Round to four decimal places as​ needed.)

This problem can be solved using the binomial probability formula because we are dealing with independent trials with only two possible outcomes: either the selected adult regrets being too young when they got the tattoo, or they do not.

The binomial probability formula is:

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

Where:
- \( n \) is the number of trials (in this case, 7 adults),
- \( k \) is the number of successes (in this case, the number of adults who say they were too young),
- \( p \) is the probability of success (12% or 0.12 in this case),
- \( 1 - p \) is the probability of failure (88% or 0.88 in this case).

### Part a: Probability that none of the selected adults say they were too young.
We want to find the probability that none of the 7 adults say they were too young, which corresponds to \( k = 0 \).

\[
P(X = 0) = \binom{7}{0} (0.12)^0 (0.88)^7
\]

Simplifying the binomial coefficient and the powers:

\[
P(X = 0) = 1 \times 1 \times (0.88)^7
\]

Now, let's calculate \( (0.88)^7 \):

\[
P(X = 0) = (0.88)^7 \approx 0.4228
\]

Thus, the probability that none of the selected adults say they were too young is approximately **0.4228**.

Would you like to continue with the remaining parts of the problem? Here are five relative questions:

1. What is the probability that exactly one adult says they were too young?
2. What is the probability that at least one adult says they were too young?
3. How does the binomial distribution differ from other probability distributions?
4. What is the expected number of adults who say they were too young?
5. How would the probability change if the percentage of adults who regret being too young increases?

**Tip**: When solving binomial problems, always verify the number of trials and probability values before calculating.

Based on a poll, among adults who regret getting tattoos, 12% 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. Part a: Find the probability that none of the selected adults say that they were too young to get tattoos. (Round to four decimal places as needed.)

Calculate the probability that none of 7 randomly selected adults regret being too young when getting tattoos, using binomial distribution. Explore key probability concepts with a step-by-step breakdown of the binomial probability formula. Perfect for students in 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