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
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eBooks | ? | ? | 120
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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 find the number of people who chose books and brownies, we can multiply the probability of choosing books by the probability of choosing brownies if the two events were independent.
The probability of choosing books is given by the ratio of the number of people who chose books to the total number of people:
P(Books) = 280/400 = 0.7
The probability of choosing brownies is given by the ratio of the number of people who chose brownies to the total number of people:
P(Brownies) = 280/400 = 0.7
If the two events were independent, the probability of choosing both books and brownies would be the product of the probabilities of each event:
P(Books and Brownies) = P(Books) * P(Brownies) = 0.7 * 0.7 = 0.49
To find the number of people who chose books and brownies, we can multiply the probability by the total number of people:
Number of people = P(Books and Brownies) * Total number of people = 0.49 * 400 = 196
Therefore, the number of people who chose books and brownies if the two events were independent is 196.
The correct answer is not provided in the options listed.