Question

based on a poll, among adults who regret getting tattoos, 15% say that they were too young when they got their tattoos. assume that nine adults who regret getting tattoos are randomly selected, and find the indicated probability. complete parts (a) through (d) below.
a. find the probability that none of
0.2316 (round to four decimal pla
at most 1
that they were too young to get tattoos
b. find the probability that exactly 0
less than 1
says that he or she was too young to get tattoos
0.3679 (round to four decimal pla
at least 1
c. find the probability that the numb
0.5995 (round to four decimal pla
exactly 1
ming they were too young is 0 or 1
d. if we randomly select nine adults,
more than 1
number who say that they were too young to get tattoos?
no, because the probability that
of the selected adults say that they were too young is 0.05

Explanation:

Step1: Identify the probability of success and number of trials

The probability $p$ that an adult who regrets getting a tattoo says they were too young is $p = 0.15$, and the number of trials $n=9$.

Step2: Use the binomial - probability formula $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$

a. Probability that none of them say they were too young ($k = 0$)

$P(X = 0)=C(9,0)\times(0.15)^{0}\times(1 - 0.15)^{9-0}$
$C(9,0)=\frac{9!}{0!(9 - 0)!}=1$, $(0.15)^{0}=1$, $(1 - 0.15)=0.85$
$P(X = 0)=1\times1\times(0.85)^{9}\approx0.2316$

b. Probability that exactly one says they were too young ($k = 1$)

$P(X = 1)=C(9,1)\times(0.15)^{1}\times(1 - 0.15)^{9 - 1}$
$C(9,1)=\frac{9!}{1!(9 - 1)!}=\frac{9!}{1!8!}=9$
$P(X = 1)=9\times0.15\times(0.85)^{8}\approx0.3679$

c. Probability that the number is 0 or 1

$P(X=0\ or\ X = 1)=P(X = 0)+P(X = 1)$
$P(X=0\ or\ X = 1)\approx0.2316+0.3679 = 0.5995\approx0.5996$

d. To determine if it is unusual

The probability that more than 1 says they were too young is $P(X>1)=1 - P(X\leq1)=1 - 0.5996 = 0.4004>0.05$
So, it is not unusual. The probability that more than 1 of the selected adults say that they were too young is greater than 0.05.

Answer:

a. $0.2316$
b. $0.3679$
c. $0.5996$
d. more than 1; greater than