Assuming there are n= 50,000 couples in the los ángeles area, what is the probability that more than one of them has the characteristics listed in the table? P( X > 1) = (c) Now let $ n $ represent the number of couples in the Los Angeles area who could have committed the crime. Let $ p $ represent the probability that a randomly selected couple has all 6 characteristics listed in the table. Assuming that the random variable $ X $ follows the binomial probability function, we have:\[P(X) = C(n,x) \cdot p^x \cdot (1-p)^{n-x}, \, x = 0, 1, 2, \ldots, n\]**Note:** Use the calculator link [http://stattrek.com/online-calculator/binomial.aspx](http://stattrek.com/online-calculator/binomial.aspx)Assuming there are $ n = 50,000 $ couples in the Los Angeles area, what is the probability that more than one of them has the characteristics listed in the table?\[P(X > 1) =\]**Explanation:**The problem describes a binomial probability scenario where you're given the total number of trials ($ n = 50,000 $) and the probability of a single success ($ p $), and we're asked to find the probability of more than one success ($ X > 1 $). The provided formula helps to compute the probability for various values of $ X $, while the calculator link is a tool for solving such a complex probability calculation.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assuming there are n= 50,000 couples in the los ángeles area, what is the probability that more than one of them has the characteristics listed in the table?

P( X > 1) =

(c) Now let $ n $ represent the number of couples in the Los Angeles area who could have committed the crime. Let $ p $ represent the probability that a randomly selected couple has all 6 characteristics listed in the table. Assuming that the random variable $ X $ follows the binomial probability function, we have:

\[
P(X) = C(n,x) \cdot p^x \cdot (1-p)^{n-x}, \, x = 0, 1, 2, \ldots, n
\]

**Note:** Use the calculator link [http://stattrek.com/online-calculator/binomial.aspx](http://stattrek.com/online-calculator/binomial.aspx)

Assuming there are $ n = 50,000 $ couples in the Los Angeles area, what is the probability that more than one of them has the characteristics listed in the table?

\[
P(X > 1) =
\]

**Explanation:**
The problem describes a binomial probability scenario where you're given the total number of trials ($ n = 50,000 $) and the probability of a single success ($ p $), and we're asked to find the probability of more than one success ($ X > 1 $). The provided formula helps to compute the probability for various values of $ X $, while the calculator link is a tool for solving such a complex probability calculation.

Expert Solution

Step 1

Obtain the probability that more than one of the 50,000 couples has all the listed characteristics:

Here, n = 50,000 and p = 0.0000000833.

Denote the number of couples who have all the listed characteristics as X.

Here, X ~ B(50,000, 0.0000000833).

The probability that more than one of the 50,000 couples has all the characteristics is obtained as 0.0000086 from the calculation given below:

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