Questions: 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)
Transcript text: a. Find the probability that none of the selected adults say that they were too young to get tattoos $\square$ (Round to four decimal places as needed)
Solution
Solution Steps
Step 1: Define the Problem
We need to find the probability that none of the selected adults say that they were too young to get tattoos. This can be modeled using a binomial distribution where:
n=25 (the number of trials, or selected adults),
x=0 (the number of successes, or adults saying they were too young),
p=0.29 (the probability of success, or saying they were too young),
q=1−p=0.71 (the probability of failure, or not saying they were too young).
Step 2: Apply the Binomial Probability Formula
The probability of exactly x successes in n trials is given by the formula:
P(X=x)=(xn)⋅px⋅qn−x
Substituting the values into the formula:
P(X=0)=(025)⋅(0.29)0⋅(0.71)25
Step 3: Calculate the Probability
Calculating each component:
(025)=1
(0.29)0=1
(0.71)25≈0.0002
Thus, we have:
P(X=0)=1⋅1⋅0.0002=0.0002
Final Answer
The probability that none of the selected adults say they were too young to get tattoos is: