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This problem deals with a binomial probability scenario.

### Given:
- **Probability (p)** that a person uses a smartphone in meetings or classes: \( p = 0.47 \)
- **Number of trials (n)**: \( n = 10 \) (since 10 adults are selected)
- We need to find the probability that **at least 5** of the selected adults use their smartphones in meetings or classes.

### Solution Strategy:
To calculate the probability of "at least 5" using their smartphones, we'll sum the probabilities for 5, 6, 7, 8, 9, and 10 using the binomial probability formula:

\[
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
\]
Where:
- \( n \) is the total number of trials (10 in this case),
- \( k \) is the number of successes (number of people using smartphones),
- \( p \) is the probability of success (0.47),
- \( 1 - p = 0.53 \) is the probability of failure.

Instead of calculating each probability manually, a more efficient way is to calculate the **complement** of the event. The complement of "at least 5" is "fewer than 5." So:

\[
P(X \geq 5) = 1 - P(X < 5)
\]

Thus, we calculate \( P(X < 5) \), which is the sum of the probabilities for 0, 1, 2, 3, and 4 people using their smartphones.

Let me compute this for you:The probability that at least 5 of the 10 selected adults use their smartphones in meetings or classes is **0.5474** (rounded to four decimal places).

Would you like further details or have any questions? Here are five related questions you might explore:

1. What is the probability that exactly 5 of the adults use their smartphones in meetings or classes?
2. How does the probability change if only 8 adults are selected instead of 10?
3. What if the percentage of adults using smartphones changes to 60%? How does this affect the outcome?
4. Can this problem be modeled using a normal approximation?
5. What is the expected number of adults using smartphones if 10 adults are selected?

**Tip:** When dealing with binomial probabilities, calculating the complement (like we did here) often simplifies the process for "at least" or "more than" cases.

Assume that when adults with smartphones are randomly selected, 47% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that at least 5 of them use their smartphones in meetings or classes.

Find the probability that at least 5 out of 10 randomly selected adult smartphone users use their devices in meetings or classes, assuming 47% of adults use them in such situations. This problem involves binomial distribution and probability concepts, making it ideal for students in Grades 11-12 or college.

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