Question

Based on a​ poll, among adults who regret getting​ tattoos, 12​% say that they were too young when they got their tattoos. Assume that ten adults who regret getting tattoos are randomly​ selected, and find the indicated probability.

Required:
a. Find the probability that the number of selected adults saying they were too young is 0 or 1.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that none of the selected adults say that they were too young to get tattoos.

Answer 1

a. 0.6588

b. 0.3978

c. 0. 279

Explanation:

In the given question the success and failure are given the number of outcomes is fixed so binomial distribution can be applied.

Here success= p = 12 % or 12/100 = 0.12

failure = q= 1-p = 1-0.12 = 0.88

n= 10

Using binomial probability distribution

a. Probability that the number of selected adults saying they were too young is 0 or 1 is calculated as:

P (x=0,1) = 0.12 ⁰(0.88)¹⁰10 C0 + 0.12 (0.88)⁹ 10 C1= 1* 0.279 * 1 + 0.12 ( 0.3165) 10 = 0. 279 + 0.3978= 0.6588

b. Probability that exactly one of the selected adults says that he or she was too young to get tattoos is calculated as

P (x=1) = 0.12 (0.88)⁹ 10 C1= 0.12 ( 0.3165) 10 = 0.3978

c. Probability that none of the selected adults say that they were too young to get tattoos is

P (x=0) = 0.12 ⁰(0.88)¹⁰10 C0 = 1* 0.279 * 1 = 0. 279