(a). The probability that no one has done one time fling is
.
(b). The probability that at least one person has done one time fling is
.
(c). The probability that no more than two person has done one time fling is
.
Further explanation:
Given:
If a person purchased an article of clothing and worn the cloths once then returned the clothes this is known as one time fling.
About
adults do one time fling.
Concept used:
The probability of an event
can be calculated as follows:
![\boxed{P(E)=\dfrac{n(E)}{n(S)}}](https://tex.z-dn.net/?f=%5Cboxed%7BP%28E%29%3D%5Cdfrac%7Bn%28E%29%7D%7Bn%28S%29%7D%7D)
Here,
is the number of favorable outcomes in an event
and
is the number of element in sample space
.
The probability of exactly
success in
trial can be expressed as follows:
![\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}](https://tex.z-dn.net/?f=%5Cboxed%7BP%28F%29%3D%5E%7Bn%7DC_%7Br%7Dp%5E%7Br%7Dq%5E%7Bn-r%7D%7D)
Here,
is the probability of success in an event and
is the probability of failure.
Calculation:
Part (a):
The probability that adults do one time fling is
.
The probability that no adult do one time fling is calculated as follows:
![\boxed{1-0.15=0.85}](https://tex.z-dn.net/?f=%5Cboxed%7B1-0.15%3D0.85%7D)
There are
adult friends in a group.
Consider
as an event that no one has done one time fling in a group of seven friends and
as the probability of an event
.
The probability
can be calculated as follows:
![\begin{aligned}P(A)&=^7C_{0}\cdot (0.15)^{0} \cdot (0.15)^{7-0}\\&=\dfrac{7!}{0!\cdot 7!}\cdot 1\cdot (0.85)^{7}\\&=1\cdot 1\cdot 0.377\\&=0.377\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DP%28A%29%26%3D%5E7C_%7B0%7D%5Ccdot%20%280.15%29%5E%7B0%7D%20%5Ccdot%20%280.15%29%5E%7B7-0%7D%5C%5C%26%3D%5Cdfrac%7B7%21%7D%7B0%21%5Ccdot%207%21%7D%5Ccdot%201%5Ccdot%20%280.85%29%5E%7B7%7D%5C%5C%26%3D1%5Ccdot%201%5Ccdot%200.377%5C%5C%26%3D0.377%5Cend%7Baligned%7D)
Therefore, the probability
is
.
Part (b):
Consider
as a complement event of an event
.
The complement of event
is the event that at least one person has done one time fling in a group of
friends.
The probability of event
can be calculated as follows:
…… (1)
Substitute
in the equation (1) to obtain the probability as follows:
Therefore, the probability that at least one person has done one time fling in a group of
friends is
.
Part (c):
The probability that no one has done one time fling is
.
Consider
as an event that one person has done one time fling in a group of seven friends and
as the probability of an event
.
The probability
can be calculated as follows:
![\begin{aligned}P(B)&=^7C_{1}\cdot (0.15)^{1} \cdot (0.85)^{7-1}\\&=\dfrac{7!}{1!\cdot 6!}\cdot (0.15) \cdot (0.85)^{6}\\&=\dfrac{7!}{6!}\cdot 0.15 \cdot 0.37714\\&=7\cdot 0.0565\\&=0.396\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DP%28B%29%26%3D%5E7C_%7B1%7D%5Ccdot%20%280.15%29%5E%7B1%7D%20%5Ccdot%20%280.85%29%5E%7B7-1%7D%5C%5C%26%3D%5Cdfrac%7B7%21%7D%7B1%21%5Ccdot%206%21%7D%5Ccdot%20%280.15%29%20%5Ccdot%20%280.85%29%5E%7B6%7D%5C%5C%26%3D%5Cdfrac%7B7%21%7D%7B6%21%7D%5Ccdot%200.15%20%5Ccdot%200.37714%5C%5C%26%3D7%5Ccdot%200.0565%5C%5C%26%3D0.396%5Cend%7Baligned%7D)
Consider
as an event that exactly two person has done one time fling in a group of seven friends and
as the probability of an event
.
The probability
can be calculated as follows:
Now, the probability that no more than two person has done one time fling in a group of
friends can be calculated as follows:
…… (2)
Substitute
,
and
in the equation (1) to obtain the probability
as follows:
![\begin{aligned}P(X)&=0.377+0.396+0.20979\\&=0.98279\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DP%28X%29%26%3D0.377%2B0.396%2B0.20979%5C%5C%26%3D0.98279%5Cend%7Baligned%7D)
Therefore, the probability that no more than two person has done one time fling is
.
Learn more:
1. Learn more about problem on numbers: brainly.com/question/1852063
2. Learn more about problem on function brainly.com/question/3225044
Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, one time fling, clothes, person, P(E)=n(E)/n(S).