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AleksandrR [38]
3 years ago
11

The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party,

and then returned the purchase? This is called a one-time fling. About 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of seven adult friends, find the following probabilities.. (a) No one has done a one-time fling. (Use 3 decimal places.). (b) At least one person has done a one-time fling. (Use 3 decimal places.). . ( c) No more than two people have done a one-time fling. (Use 3 decimal places.)
Mathematics
2 answers:
Nuetrik [128]3 years ago
6 0
<span>Using the binomial probability formula

b(x; n, p) = p^x * nCx * (1-P)^(n-x)

Where: 
x = flings 
n = sample size 

A) </span><span>b(0; 8, .15)
= (0.15)^0 * (8C0) * (.85^8) </span>
<span>= 1 * 1 *.272 </span>
<span>= .272 

B) = 1 - A
= 1 - 0.272
= 0.728

C) </span><span>b(1; 8, .15)
= (.15^1) * (8C1) * (.85^7 )</span>
<span>= .385 
</span>
<span>b(2; 8, .15)
= (.15^2) * (8C2) * (.85^6) </span>
<span>= .238 
</span>
<span>b ≤ 2 = A + b1 + b2</span>
<span>= .272 + .385 + .238 </span>
<span>= .895</span>
blagie [28]3 years ago
3 0

(a). The probability that no one has done one time fling is \boxed{\bf 0.377}.

(b). The probability that at least one person has done one time fling is \boxed{\bf 0.623}.

(c). The probability that no more than two person has done one time fling is \boxed{\bf 0.98279}.

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 15\% adults do one time fling.

Concept used:

The probability of an event E can be calculated as follows:

\boxed{P(E)=\dfrac{n(E)}{n(S)}}

Here, n(E) is the number of favorable outcomes in an event E and n(S) is the number of element in sample space S.

The probability of exactly r success in n trial can be expressed as follows:

\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}

Here, p is the probability of success in an event and q is the probability of failure.

Calculation:

Part (a):

The probability that adults do one time fling is 0.15.

The probability that no adult do one time fling is calculated as follows:

\boxed{1-0.15=0.85}

There are 7 adult friends in a group.

Consider A as an event that no one has done one time fling in a group of seven friends and P(A) as the probability of an event A.

The probability P(A) 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}

Therefore, the probability P(A) is \boxed{\bf 0.377}.

Part (b):

Consider A' as a complement event of an event A.

The complement of event A is the event that at least one person has done one time fling in a group of 7 friends.

The probability of event A' can be calculated as follows:

\boxed{P(A')=1-P(A)}      …… (1)

Substitute P(A)=0.377 in the equation (1) to obtain the probability   as follows:

\begin{aligned}P(A')&=1-0.377\\&=0.623\end{aligned}  

Therefore, the probability that at least one person has done one time fling in a group of 7 friends is \boxed{\bf 0.623}.

Part (c):

The probability that no one has done one time fling is 0.377.

Consider B as an event that one person has done one time fling in a group of seven friends and P(B) as the probability of an event B.

The probability P(B) 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}

 

Consider C as an event that exactly two person has done one time fling in a group of seven friends and P(C) as the probability of an event C.

The probability P(C) can be calculated as follows:

\begin{aligned}P(C)&=^7C_{2}\cdot (0.15)^{2} \cdot (0.85)^{7-2}\\&=\dfrac{7!}{2!\cdot 5!}\cdot (0.15)^{2}\cdot (0.85)^{5}\\&=\dfrac{7\cdot 6}{2}\cdot 0.0225\cdot 0.444\\&=21\cdot 0.00999\\&=0.20979\end{aligned}  

Now, the probability that no more than two person has done one time fling in a group of 7 friends can be calculated as follows:

\boxed{P(X)=P(A)+P(B)+P(C)}         …… (2)

Substitute P(A)=0.377, P(B)=0.396 and P(C)=0.209 in the equation (1) to obtain the probability P(X) as follows:

\begin{aligned}P(X)&=0.377+0.396+0.20979\\&=0.98279\end{aligned}

Therefore, the probability that no more than two person has done one time fling is \boxed{\bf 0.98279}.

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).

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