To predict the number of people at the reception whose favorite snack will be brownies, follow these steps:
1. Calculate the total number of people in the sample:
- Add up the number of people for each snack category.
[tex]\[
42 (\text{Brownies}) + 18 (\text{Cookies}) + 51 (\text{Chips}) + 64 (\text{Other})
\][/tex]
- Thus, the total sample size is:
[tex]\[
42 + 18 + 51 + 64 = 175
\][/tex]
2. Determine the probability that a person's favorite snack is brownies:
- The number of people who prefer brownies is 42.
- Divide this by the total sample size to find the probability.
[tex]\[
\text{Probability (Brownies)} = \frac{42}{175}
\][/tex]
- Calculating this gives:
[tex]\[
\frac{42}{175} = 0.24
\][/tex]
3. Use the probability to predict the number of attendees preferring brownies:
- The total number of attendees at the reception is 3400.
- Multiply the total number of attendees by the probability that a person's favorite snack is brownies.
[tex]\[
\text{Predicted Number of Brownie Lovers} = 0.24 \times 3400
\][/tex]
- Calculating this gives:
[tex]\[
0.24 \times 3400 = 816.0
\][/tex]
4. Round the result to the nearest whole number:
- The prediction from the previous step is already a whole number, so no further rounding is necessary.
Therefore, the predicted number of people at the reception whose favorite snack will be brownies is:
[tex]\[
\boxed{816}
\][/tex]
