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Lina20 [59]
3 years ago
13

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 eight adult friends, what is the probability of the following?
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
Mathematics
1 answer:
Mama L [17]3 years ago
4 0

Answer:

(a)\ P(x = 0) = 0.2725

(b)\ P(x \ge 1) =0.7275

(c)\ P(x \le 2) = 0.8948

Step-by-step explanation:

Given

n = 8 --- 8 friends

p = 15\% --- proportion that one-time fling

This question is an illustration of binomial probability, and it is represented as:

P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}

Solving (a): P(x = 0) --- None has done one time fling

P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}

P(x = 0) = 1* 1 * (1 - 0.15)^{8}

P(x = 0) = 0.85^8

P(x = 0) = 0.2725

Solving (b): P(x \ge 1)

To do this, we make use of compliment rule:

P(x = 0) + P(x \ge 1) =1

Rewrite as:

P(x \ge 1) =1 - P(x = 0)

P(x \ge 1) =1 - 0.2725

P(x \ge 1) =0.7275

Solving (c): P(x\le 2)--- Not more than 2 has one time fling

This is calculated as:

P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

We have:

P(x = 0) = 0.2725

P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}

P(x = 1) = 8* (0.15) * (1 - 0.15)^7

P(x = 1) = 0.3847

P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}

P(x = 2) = 28* (0.15)^2 * (1-0.15)^6

P(x = 2) = 0.2376

So:

P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

P(x \le 2) = 0.2725 + 0.3847 + 0.2376

P(x \le 2) = 0.8948

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