https://file.aiquickdraw.com/mathbot/file/1727672296442nmwg0lm1.jpg

The problem in the image asks for the probability that a person chosen at random does *not* believe that people can see the future in their dreams, based on a survey. Here's a breakdown of the problem:

- **410** people responded "yes" (they believe people can see the future in their dreams).
- **418** people responded "no" (they do not believe people can see the future in their dreams).

We need to find the probability that a randomly chosen person does not believe in seeing the future in dreams, i.e., they responded "no".

### Total number of people surveyed:
\[
\text{Total people} = 410 (\text{yes}) + 418 (\text{no}) = 828
\]

### Probability of selecting a person who responded "no":
\[
\text{Probability} = \frac{\text{Number of "no" responses}}{\text{Total number of people}} = \frac{418}{828}
\]

Now, I'll calculate this probability and round to four decimal places.The probability that a randomly chosen person does not believe people can see the future in their dreams is **0.5048** (rounded to four decimal places).

Would you like more details or have any questions about this? 

Here are five related questions to consider:
1. How would the probability change if the number of "no" responses increased by 10?
2. What is the probability that a randomly chosen person believes people *can* see the future in their dreams?
3. If the total number of survey participants doubled, but the proportion of "yes" and "no" responses remained the same, what would be the new probability?
4. How would you calculate the probability if the total number of people surveyed was unknown?
5. What would happen to the probability if there were an equal number of "yes" and "no" responses?

**Tip:** When calculating probabilities, always ensure that the total number of possible outcomes is accurately accounted for to avoid errors.

A group of people were asked if some people see the future in their dreams. 410 responded 'yes,' and 418 responded 'no.' Find the probability that if a person is chosen at random, the person does NOT believe some people see the future in their dreams.

Find the probability that a randomly chosen person does not believe people can see the future in dreams, given that 410 people said 'yes' and 418 said 'no.' This problem applies basic probability concepts and is suitable for Grades 5-7.

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