Assume that when adults with smartphones are randomly​ selected, 59% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that at least 5 of them use their smartphones in meetings or classes.


We can solve this problem using the **binomial probability formula**, since we are dealing with a fixed number of trials (7 adult smartphone users) and two possible outcomes for each trial: either the adult uses their smartphone in meetings or classes or they do not.

The binomial probability formula is:

\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]

Where:
- \( n \) is the total number of trials (in this case, \( n = 7 \)),
- \( k \) is the number of successful trials (in this case, \( k = 5, 6, \text{or} 7 \)),
- \( p \) is the probability of success on a single trial (in this case, \( p = 0.59 \)),
- \( 1-p \) is the probability of failure,
- \( \binom{n}{k} \) is the binomial coefficient, which is calculated as \( \frac{n!}{k!(n-k)!} \).

### We need to find the probability of at least 5 adults using their smartphones in meetings or classes, which means we need to calculate:
\[
P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)
\]

Let’s compute each probability step-by-step. I'll now calculate the exact values for you.The probability that at least 5 of the 7 selected adult smartphone users use their smartphones in meetings or classes is approximately **0.398** or **39.8%**.

Would you like more details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How would the probability change if the selection involved more adults (e.g., 10 adults)?
2. What if the probability of using smartphones in meetings increased to 70%? How would that affect the result?
3. Can you calculate the probability of exactly 6 adults using their smartphones in meetings?
4. How do we interpret the binomial coefficient in this context?
5. How would you modify this problem if there were 3 possible outcomes instead of 2?

**Tip:** When working with binomial probabilities, always ensure the trials are independent and the probability of success remains constant across all trials.

Assume that when adults with smartphones are randomly​ selected, 59% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that at least 5 of them use their smartphones in meetings or classes.

Calculate the probability that at least 5 out of 7 randomly selected adults use their smartphones in meetings, given a 59% usage rate. This problem applies binomial probability, providing step-by-step calculations and analysis, suitable for Grades 10-12.

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