mustache and beard and also drove a yellow car. Based on this evidenCE THE PUNCO alTUJIu Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case against the defendants. The probabilities listed below were presented by the prosecution for the known characteristics of the thieves. Characteristic Probability Yellow car 1/10 Man with mustache 1/4 Woman with ponytail 1/10 Woman with blonde hair 1/3 Man with beard 1/10 Interracial couple in a car 1/1000 (a) Assuming that the characteristics listed above are independent of each other, what is the probabilit a randomly selected couple has all these characteristics? That is what is, calculate the probability: P( "yellow car" and "man w/ mustache, beard and ... "interracial couple in car") (b) Based on the above result would you convict the defendant? Explain thoroughly. ) Now let n represent the number of couples in the Los Angeles area who could have committed the (c) 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) ' P* (1-p)"-x, x 0, 1, 2, ...n %3D Note: Use the calculator link http://stattrek.com/online-calculator/binomialaspx 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? %3D P(X > 1) = (d) Does this result cause you to change your mind regarding the defendant's guilt? Explain. (e) The probability that more than one couple has these characteristics assuming there is at least one couple is given by the formula below and each is evaluated with the binomial formula from (c). P(X >1 |X > 1) = P(X > 1) %3D %3D P(X 21) (f) Do you think the couple should be convicted "beyond all reasonable doubt" based on the answer fror part (e)? Explain why or why not.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
icon
Concept explainers
Question
100%

According to the graph part c,d,e, and f 

mustache and beard and also drove a yellow car. Based on this evidenCE THE PUNCO alTUJIu
Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case
against the defendants. The probabilities listed below were presented by the prosecution for the known
characteristics of the thieves.
Characteristic
Probability
Yellow car
1/10
Man with mustache
1/4
Woman with ponytail
1/10
Woman with blonde hair
1/3
Man with beard
1/10
Interracial couple in a car
1/1000
(a) Assuming that the characteristics listed above are independent of each other, what is the probabilit
a randomly selected couple has all these characteristics? That is what is, calculate the probability:
P( "yellow car" and "man w/ mustache, beard and ... "interracial couple in car")
(b) Based on the above result would you convict the defendant? Explain thoroughly.
Transcribed Image Text:mustache and beard and also drove a yellow car. Based on this evidenCE THE PUNCO alTUJIu Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case against the defendants. The probabilities listed below were presented by the prosecution for the known characteristics of the thieves. Characteristic Probability Yellow car 1/10 Man with mustache 1/4 Woman with ponytail 1/10 Woman with blonde hair 1/3 Man with beard 1/10 Interracial couple in a car 1/1000 (a) Assuming that the characteristics listed above are independent of each other, what is the probabilit a randomly selected couple has all these characteristics? That is what is, calculate the probability: P( "yellow car" and "man w/ mustache, beard and ... "interracial couple in car") (b) Based on the above result would you convict the defendant? Explain thoroughly.
) Now let n represent the number of couples in the Los Angeles area who could have committed the
(c)
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) ' P* (1-p)"-x, x 0, 1, 2, ...n
%3D
Note: Use the calculator link http://stattrek.com/online-calculator/binomialaspx
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?
%3D
P(X > 1) =
(d) Does this result cause you to change your mind regarding the defendant's guilt? Explain.
(e) The probability that more than one couple has these characteristics assuming there is at least one couple
is given by the formula below and each is evaluated with the binomial formula from (c).
P(X >1 |X > 1) =
P(X > 1)
%3D
%3D
P(X 21)
(f) Do you think the couple should be convicted "beyond all reasonable doubt" based on the answer fror
part (e)? Explain why or why not.
Transcribed Image Text:) Now let n represent the number of couples in the Los Angeles area who could have committed the (c) 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) ' P* (1-p)"-x, x 0, 1, 2, ...n %3D Note: Use the calculator link http://stattrek.com/online-calculator/binomialaspx 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? %3D P(X > 1) = (d) Does this result cause you to change your mind regarding the defendant's guilt? Explain. (e) The probability that more than one couple has these characteristics assuming there is at least one couple is given by the formula below and each is evaluated with the binomial formula from (c). P(X >1 |X > 1) = P(X > 1) %3D %3D P(X 21) (f) Do you think the couple should be convicted "beyond all reasonable doubt" based on the answer fror part (e)? Explain why or why not.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON