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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 10% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of ten adult friends, what is the probability of the following? (Round your answers to three decimal places.)

a. no one has done a one time fling
b. at least one person has done a one time fling
c. no more than two people have done a one time fling

Respuesta :

Answer:

a. 0.349

b. 0.651

c. 0.93

Step-by-step explanation:

According to the Question,

  • Given, About 10% of all adults deliberately do a one-time fling and In a group of ten adult friends.

Thus, p=0.10 , n=10 &  [tex]\left[\begin{array}{ccc}n\\x\\\end{array}\right] = \frac{n!}{x!(n-x)!}[/tex]  

Now, Use Binomial distribution = [tex]\left[\begin{array}{ccc}n\\x\\\end{array}\right]*(p)^{x} *{(1-p)}^{n-x}[/tex]

a. p(x=0) ⇒  [tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right]*(0.1)^{0} *{(0.9)}^{10}[/tex] = 0.349  

Thus, The Probability that No one has done a one-time fling = 0.349

b. p(x≥1) = 1 - p(x=0)   ⇒   1 - 0.349 = 0.651

Thus, The Probability that at least one person has done a one-time fling = 0.651

c. p(x≤2) = p(x=0) + p(x=1) + p(x=2)

p(x≤2) = [tex]\left[\begin{array}{ccc}10\\0\\\end{array}\right]*(0.1)^{0} *{(0.9)}^{10}[/tex] + [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right]*(0.1)^{1} *{(0.9)}^{9}[/tex] + [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right]*(0.1)^{2} *{(0.9)}^{8}[/tex]

on Solving, we get

p(x≤2) = 0.349 + 0.347 + 0.194

p(x≤2) = 0.93

Thus, The Probability that No More Than two person have done a one-time fling = 0.93

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