Question

In: Statistics and Probability

In a survey of 177 people, the following data were obtained relating gender to color-blindness: Color-Blind...

In a survey of 177 people, the following data were obtained relating gender to color-blindness:

	Color-Blind (C)	Not Color - Blind	Total
Male (M)	92	36	128
Female (F)	33	16	49
Total	125	52	177

A person is randomly selected. What is the probability that the person is:
a) Male?
b) Male and Color-blind?
c) Male given that the person is Color-blind?
d) Color-blind given that the person is Male?
e) Female given that the person is not Color-blind?
f) Are the events Male and Color blind independent?  Enter yes or no.

Solutions

Expert Solution

Total number of people = 177

Number of male = 128

Probability that the person is Male = (Number of male Total number of people) = (128 177) = 0.7232

Answer: 0.7232

Number of Male and Color-blind = 92

Probability that the person is Male and Color-blind = (Number of Male and Color-blind Total number of people)

Probability that the person is Male and Color-blind = (92 177) = 0.5198

Answer: 0.5198

Number of Male and Color-blind = 92

Number of Color-blind = 125

Probability that the person is Male given that the person is Color-blind = (Number of Male and Color-blind Number of Color-blind)

Probability that the person is Male given that the person is Color-blind = (92 125) = 0.736

Answer: 0.736

Number of Male and Color-blind = 92

Number of Male = 128

Probability that the person is Color-blind given that the person is Male = (Number of Male and Color-blind Number of Male)

Probability that the person is Color-blind given that the person is Male = (92 128) = 0.7187

Answer: 0.7187

Number of Female and not Color-blind = 16

Number of Not Color-blind = 52

Probability that the person is Female given that the person is not Color-blind = (Number of Female and not Color-blind Number of Not Color-blind )

Probability that the person is Female given that the person is not Color-blind = (16 52) = 0.3077

Answer: 0.3077

If the events Male and Color blind are independent then probability that the person is Male and Color-blind will be equal to the product of probability that the person is Male and probability that the person is Color-blind

We write the above statement in equation form for understanding

If probability that the person is Male and Color-blind = (probability that the person is Male probability that the person is Color-blind) then events Male and Color blind are independent

we know the values of probability from above question except probability that the person is Color-blind

probability that the person is Color-blind = (Number of Color-blind Total number of people) =(125 177) =0.7062

(probability that the person is Male probability that the person is Color-blind) = 0.7232 0.7062 = 0.5107

0.5198 0.5107

So, probability that the person is Male and Color-blind (probability that the person is Male probability that the person is Color-blind)

Therefore, events Male and Color blind are not independent

Answer : no.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In a survey of 233 people, the following data were obtained relating gender to political orientation:...

In a survey of 233 people, the following data were obtained relating gender to political orientation: Republican (R) Democrat (D) Independent (I) Total Male (M) 64 37 16 117 Femal (F) 50 50 16 116 Total 114 87 32 233 A person is randomly selected. What is the probability that the person is: a) Male? b) Male and a Democrat? c) Male given that the person is a Democrat? d) Republican given that the person is Male? e) Female given...

In a survey of 233 people, the following data were obtained relating gender to political orientation:...

In a survey of 233 people, the following data were obtained relating gender to political orientation: Republican (R) Democrat (D) Libertarian (L) Total Male (M) 53 55 7 115 Female (F) 62 44 12 118 Total 115 99 19 233 A person is randomly selected. What is the probability that the person is: a) Male? b) Male and a Democrat? c) Male given that the person is a Democrat? d) Republican given that the person is Male? e) Female given...

a) Color blindness is an X-linked trait. A female who is color blind marries a male...

a) Color blindness is an X-linked trait. A female who is color blind marries a male with no history of the condition. Show the problem. Of their children, what proportion would be expected to be color blind? Are these sons or daughters or both? Are any children carriers (having the gene, but not expressing the condition)? Are these sons or daughters or both? b)In sea horses long tail is dominant to short, and thick scales is dominant to thin. Cross...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average female CEOs have higher salaries than male CEOs at the 0.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Salary Experience Female (1 if female, 0 if...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs at the 0.010.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Male (1...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use...

Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs at the 0.050.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Male (1...

In a recent survey, the following data were obtained in response to the question “When making...

In a recent survey, the following data were obtained in response to the question “When making a purchase, do you prefer to pay with cash or a credit card?” The responses are listed in the table. Gender Cash Credit Card Total Males 21 39 60 Females 15 25 40 Total 36 64 100 What is the probability that a randomly selected person is a female and prefers to pay with cash?

In a survey of MBA students, the following data were obtained on “students’ first reason for...

In a survey of MBA students, the following data were obtained on “students’ first reason for application to the school in which they matriculated.” Reason for Application School School cost or Quality Convenience Other Totals Enrollment Status Full Time 421 393 76 890 Part Time 400 593 46 1039 Totals 821 986 122 1929 (a) Develop a joint probability table for these data. (b) Use the marginal probabilities of school quality, school cost or convenience, and other to comment on...

1)Red-green color blindness is a sex-linked recessive trait in humans. Two people with normal color vision...

1)Red-green color blindness is a sex-linked recessive trait in humans. Two people with normal color vision have a color-blind son. What are the genotypes of the parents? A)XnXn and XnY B)XNXN and XNY C)XNXn and XNY D)XNXN and XnY 2)A poison interferes with the action of RNA polymerase II, but not RNA polymerase I or III. Which of the following is likely to be true of a cell exposed to the poison? A)production of tRNA would be stopped but not...

Suppose we have data from a health survey conducted in year 2000. Data were obtained from...

Suppose we have data from a health survey conducted in year 2000. Data were obtained from a random sample of 1000 persons. An OLS linear regression analysis was carried out in the following way: Dependent Variable: Systolic blood pressure (SBP, in mmHg) Independent Variables: Gender (1 if female, 0 if male) Age (in years) Education (binary variables for “Not graduated from high school” and “Graduated from high school (but not from college)”; the reference category is “Graduated from college”) A...

Subjects