A survey asked what types of books and deserts people preferred. The results are summarized in this two-way frequency table.
TABLE: --------CHEESECAKE | BROWNIES | TOTAL
PAPER BOOKS| 84 -------------| ? --------------| 280
------
eBooks |------------ ?-------------- | ------------ ? | 120
-------
TOTAL |--------- 120 ---------------| 280--------- | 400
What would the number of people who chose Books and brownies be if the two events were independent?
a. 0.21
b. 84
c. 36
d. 120
To determine the number of people who chose Books and brownies if the two events were independent, we need to find the expected counts for this combination.
First, let's calculate the proportions for each category:
For Paper Books: 280 / 400 = 0.7
For eBooks: 120 / 400 = 0.3
For Cheesecake: 120 / 400 = 0.3
For Brownies: 280 / 400 = 0.7
Next, we multiply the proportions to find the expected counts:
For Books and Brownies:
Expected Count = Proportion of Books * Proportion of Brownies * Total Count
= 0.7 * 0.7 * 400
= 0.49 * 400
= 196
Therefore, the number of people who chose Books and brownies if the two events were independent would be 196, which is not listed as an option.