Holiday Shopping Macy’s Target Totals Age 29-39 35 30 65 Age 18-28 42 75 117 Totals 77 105 182 Enter answer as an unreduced fraction, using / for division using no spaces between it and the numbers. For example, 3 divided by 4 would be entered 3/4. Answer: Using the table from class today, find P(Macy’s and age 29-39) Holiday Shopping Macy’s Target Totals Age 29-39 35 30 65 Age 18-28 42 75 117 Totals 77 105 182 Enter answer as a product of two unreduced fractions, using / for division and * for multiplication, using no spaces between the operations and the numbers. For example, three fourths multiplied by five thirds would be entered 3/4*5/3.
The Correct Answer and Explanation is:
To find P(Macy’s and age 29-39)P(\text{Macy’s and age 29-39})P(Macy’s and age 29-39), we can use the joint probability formula. This formula is based on the ratio of the number of events (in this case, people who shopped at Macy’s and are between the ages of 29-39) to the total number of observations (total people in the survey).
From the table:
- The number of people who shopped at Macy’s and are in the age group 29-39 is 35.
- The total number of people surveyed is 182.
Thus, we have: P(Macy’s and age 29-39)=Number of people who shopped at Macy’s and are in age 29-39Total number of people surveyed=35182P(\text{Macy’s and age 29-39}) = \frac{\text{Number of people who shopped at Macy’s and are in age 29-39}}{\text{Total number of people surveyed}} = \frac{35}{182}P(Macy’s and age 29-39)=Total number of people surveyedNumber of people who shopped at Macy’s and are in age 29-39=18235
Now, to represent the answer as a product of two unreduced fractions, let’s break down the total number of people into two parts:
- The probability of being in the Macy’s category is 77182\frac{77}{182}18277 (since 77 people shopped at Macy’s).
- The probability of being in the age 29-39 category is 65182\frac{65}{182}18265 (since 65 people are in this age range).
To find the joint probability (shopping at Macy’s * being in the age 29-39 group), we multiply these two fractions: P(Macy’s and age 29-39)=77182∗65182P(\text{Macy’s and age 29-39}) = \frac{77}{182} * \frac{65}{182}P(Macy’s and age 29-39)=18277∗18265
This is the answer in the form of two unreduced fractions.
So, the final answer is: 77182∗65182\frac{77}{182}* \frac{65}{182}18277∗18265
This gives the joint probability as a product of two unreduced fractions.
