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76 CUVTES 3 SOME BASE PROGRAMITY CONCEPTS Solution: The variables are equal to each is broken down into categories. Early for recent (15) years ago, they (26) had taken for consent according to an age or 15 years. (27) The variable family history of noood disorders is broken down into four categories: negative family history (A), bipolar disorder only (B), impolar disorder only (C), and subspecies family who is hicogen) of both antipolar and bipolar disorder only (A), bipolar disorder only (C) and bipolar disorder only (D), and bipolar disorder only (A), bipolar disorder only (A), bipolar disorder only (B), bipolar disorder (A), bipolar disorder (B), bipolar disorder. The four four populations of the variable (a) computed are based on disorder. [ ( P(E1) )=23 / 13 ( is )-0.851 ( P(E1) )=19 / 13 ( is )-0.8597 P(E 1 C)=4 / 13 / 18 ( - ) 1.829 P(E 1 D)=0.33 / 13 ( is )-1.667 ] We obtain the marginal probability P(E 1) by adding these four ( mathrm(n) ) probabilities as follows: [ P(E 1)=P(E 1)+P(E 1)+P(E 1)+P(E 1)+P(E 1) =0.881+0.997+1.299+1.067 ] The result, as expected, is the same as the one obtained by using the marginal total for early 60 women and the total number of subjects as the denominator. [ ( Early as the numerator and the total number of subjects as the denominator. ) ] EXERCISES 3.4.1 In a study of violent victimization of women and men, Proceedity at 4.4.2-collocted information from 69 % women and 1549 men are equal to 48 to 45 years at several family posters centers in the metropolitan Descro and State Patient of Black and a health history questionnaire that included a questionnaire under the information. The following table shows the sample significance of these populations by and the other explanations for the following data. Which of the sample data is not correct about the partions (friends, parent victimization, or strangers), and doctors, victimization by persons from other patients (friends, family members, or strangers), and doctors who are reported undernthe victimization. No Millenization & Partners & Nonpartners & Multiple & Yelimization & Total Women & 611 & 34 & 16 & 16 & 679 Men & 936 & 40 & 17 & 10 & 345 Total & 193 & 14 & 12 & 28 & 104 Source: Dara provided counsel of Jose R. Twentell, Dr. Beeonary Cegan, P.D. (a) Suppose we pick a subject at random from this group. What is its probability that this subject will be? (b) What do we call the probability calculated in part a? (c) Show how to calculate the probability asked for in part a by two additional methods. EXERCISES 77 2.1) For your subject at random, what is the probability that the subject will be a woman and have experienced parent abuse? (a) What do we call the probability calculated in part a? (b) Suppose we picked an atea random. Knowing this information, what is the probability that he experiences from nonpertensive? (c) Suppose we pick a student at random. What is the probability that it is a man or someone who experienced abuse from a partner?

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76 CUVTES 3 SOME BASE PROGRAMITY CONCEPTS Solution: The variables are equal to each is broken down into categories. Early for recent (15) years ago, they (26) had taken for consent according to an age or 15 years. (27) The variable family history of noood disorders is broken down into four categories: negative family history (A), bipolar disorder only (B), impolar disorder only (C), and subspecies family who is hicogen) of both antipolar and bipolar disorder only (A), bipolar disorder only (C) and bipolar disorder only (D), and bipolar disorder only (A), bipolar disorder only (A), bipolar disorder only (B), bipolar disorder (A), bipolar disorder (B), bipolar disorder. The four four populations of the variable (a) computed are based on disorder. [ ( P(E1) )=23 / 13 ( is )-0.851 ( P(E1) )=19 / 13 ( is )-0.8597 P(E 1 C)=4 / 13 / 18 ( - ) 1.829 P(E 1 D)=0.33 / 13 ( is )-1.667 ] We obtain the marginal probability P(E 1) by adding these four ( mathrm(n) ) probabilities as follows: [ P(E 1)=P(E 1)+P(E 1)+P(E 1)+P(E 1)+P(E 1) =0.881+0.997+1.299+1.067 ] The result, as expected, is the same as the one obtained by using the marginal total for early 60 women and the total number of subjects as the denominator. [ ( Early as the numerator and the total number of subjects as the denominator. ) ] EXERCISES 3.4.1 In a study of violent victimization of women and men, Proceedity at 4.4.2-collocted information from 69 % women and 1549 men are equal to 48 to 45 years at several family posters centers in the metropolitan Descro and State Patient of Black and a health history questionnaire that included a questionnaire under the information. The following table shows the sample significance of these populations by and the other explanations for the following data. Which of the sample data is not correct about the partions (friends, parent victimization, or strangers), and doctors, victimization by persons from other patients (friends, family members, or strangers), and doctors who are reported undernthe victimization. No Millenization & Partners & Nonpartners & Multiple & Yelimization & Total Women & 611 & 34 & 16 & 16 & 679 Men & 936 & 40 & 17 & 10 & 345 Total & 193 & 14 & 12 & 28 & 104 Source: Dara provided counsel of Jose R. Twentell, Dr. Beeonary Cegan, P.D. (a) Suppose we pick a subject at random from this group. What is its probability that this subject will be? (b) What do we call the probability calculated in part a? (c) Show how to calculate the probability asked for in part a by two additional methods. EXERCISES 77 2.1) For your subject at random, what is the probability that the subject will be a woman and have experienced parent abuse? (a) What do we call the probability calculated in part a? (b) Suppose we picked an atea random. Knowing this information, what is the probability that he experiences from nonpertensive? (c) Suppose we pick a student at random. What is the probability that it is a man or someone who experienced abuse from a partner?
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76 CUVTES 3 SOME BASE PROGRAMITY CONCEPTS Solution: The variables are equal to each is broken down into categories. Early for recent (15) years ago, they (26) had taken for consent according to an age or 15 years. (27) The variable family history of noood disorders is broken down into four categories: negative family history (A), bipolar disorder only (B), impolar disorder only (C), and subspecies family who is hicogen) of both antipolar and bipolar disorder only (A), bipolar disorder only (C) and bipolar disorder only (D), and bipolar disorder only (A), bipolar disorder only (A), bipolar disorder only (B), bipolar disorder (A), bipolar disorder (B), bipolar disorder. The four four populations of the variable (a) computed are based on disorder. [ ( P(E1) )=23 / 13 ( is )-0.851 ( P(E1) )=19 / 13 ( is )-0.8597 P(E 1 C)=4 / 13 / 18 ( - ) 1.829 P(E 1 D)=0.33 / 13 ( is )-1.667 ] We obtain the marginal probability P(E 1) by adding these four ( mathrm(n) ) probabilities as follows: [ P(E 1)=P(E 1)+P(E 1)+P(E 1)+P(E 1)+P(E 1) =0.881+0.997+1.299+1.067 ] The result, as expected, is the same as the one obtained by using the marginal total for early 60 women and the total number of subjects as the denominator. [ ( Early as the numerator and the total number of subjects as the denominator. ) ] EXERCISES 3.4.1 In a study of violent victimization of women and men, Proceedity at 4.4.2-collocted information from 69 % women and 1549 men are equal to 48 to 45 years at several family posters centers in the metropolitan Descro and State Patient of Black and a health history questionnaire that included a questionnaire under the information. The following table shows the sample significance of these populations by and the other explanations for the following data. Which of the sample data is not correct about the partions (friends, parent victimization, or strangers), and doctors, victimization by persons from other patients (friends, family members, or strangers), and doctors who are reported undernthe victimization. No Millenization & Partners & Nonpartners & Multiple & Yelimization & Total Women & 611 & 34 & 16 & 16 & 679 Men & 936 & 40 & 17 & 10 & 345 Total & 193 & 14 & 12 & 28 & 104 Source: Dara provided counsel of Jose R. Twentell, Dr. Beeonary Cegan, P.D. (a) Suppose we pick a subject at random from this group. What is its probability that this subject will be? (b) What do we call the probability calculated in part a? (c) Show how to calculate the probability asked for in part a by two additional methods. EXERCISES 77 2.1) For your subject at random, what is the probability that the subject will be a woman and have experienced parent abuse? (a) What do we call the probability calculated in part a? (b) Suppose we picked an atea random. Knowing this information, what is the probability that he experiences from nonpertensive? (c) Suppose we pick a student at random. What is the probability that it is a man or someone who experienced abuse from a partner?

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### (a) $\frac{679}{1024} \approx 0.6637$<br />### (b) Marginal probability<br />### (c) Method 1: Relative frequency: $\frac{679}{1024} = 0.6637$, Method 2: Complementary probability: $1 - 0.3363 = 0.6637$<br />### (d) $\frac{34}{1024} \approx 0.0332$<br />### (e) Joint probability<br />### (f) $\frac{17}{345} \approx 0.0493$<br />### (g) Conditional probability<br />### (h) $\frac{345 + 44 - 10}{1024} = \frac{379}{1024} \approx 0.3701$

Giải thích

## Step 1: Calculate the probability that a randomly picked subject will be a woman<br />### The total number of subjects is $679 + 345 = 1024$. The number of women is 679. Therefore, the probability that a randomly picked subject will be a woman is $\frac{679}{1024}$.<br /><br />## Step 2: Identify the type of probability calculated in part (a)<br />### The probability calculated in part (a) is a marginal probability because it is the probability of a single event occurring without any condition.<br /><br />## Step 3: Calculate the probability that a randomly picked subject will be a woman using two additional methods<br />### Method 1: Using relative frequency:<br />The relative frequency of women in the sample is $\frac{679}{1024} = 0.6637$.<br />### Method 2: Using complementary probability:<br />The probability of picking a man is $\frac{345}{1024} = 0.3363$. Therefore, the probability of picking a woman is $1 - 0.3363 = 0.6637$.<br /><br />## Step 4: Calculate the probability that a randomly picked subject will be a woman and have experienced partner abuse<br />### The number of women who experienced partner abuse is 34. Therefore, the probability that a randomly picked subject will be a woman and have experienced partner abuse is $\frac{34}{1024}$.<br /><br />## Step 5: Identify the type of probability calculated in part (d)<br />### The probability calculated in part (d) is a joint probability because it is the probability of two events occurring together.<br /><br />## Step 6: Calculate the probability that a randomly picked man experienced abuse from nonpartners<br />### The number of men who experienced abuse from nonpartners is 17. The total number of men is 345. Therefore, the conditional probability that a randomly picked man experienced abuse from nonpartners is $\frac{17}{345}$.<br /><br />## Step 7: Identify the type of probability calculated in part (f)<br />### The probability calculated in part (f) is a conditional probability because it is the probability of an event occurring given that another event has already occurred.<br /><br />## Step 8: Calculate the probability that a randomly picked subject will be a man or someone who experienced abuse from a partner<br />### The number of men is 345, and the number of people who experienced abuse from a partner is 44. The number of men who experienced abuse from a partner is 10. Therefore, the probability that a randomly picked subject will be a man or someone who experienced abuse from a partner is $\frac{345 + 44 - 10}{1024}$.
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