https://file.aiquickdraw.com/mathbot/file/1729785948206bcu45med.jpg

This problem involves finding the probability that, in a sample of 8 adult smartphone users, at least 2 of them use their smartphones in meetings or classes. The percentage given is 48%, so the probability that an individual uses their smartphone in such settings is \( p = 0.48 \).

The problem requires the use of a **binomial probability distribution**, as it involves a fixed number of trials (8 adults) with two possible outcomes (uses smartphone or not).

### Steps:
1. **Identify the given information:**
   - Probability of success (using smartphone): \( p = 0.48 \).
   - Probability of failure (not using smartphone): \( q = 1 - p = 0.52 \).
   - Number of trials: \( n = 8 \).

2. **Find the probability of at least 2 successes**:
   - This means calculating \( P(X \geq 2) \).
   - Use the complement rule: \( P(X \geq 2) = 1 - P(X < 2) \).
   - \( P(X < 2) = P(X = 0) + P(X = 1) \).

3. **Calculate the required probabilities:**
   - \( P(X = 0) = \binom{8}{0} p^0 (1-p)^8 \).
   - \( P(X = 1) = \binom{8}{1} p^1 (1-p)^7 \).

### Computation:
1. \( P(X = 0) = (0.52)^8 \).
2. \( P(X = 1) = 8 \cdot (0.48)^1 \cdot (0.52)^7 \).

After calculating these, subtract the sum from 1 to get the final answer for \( P(X \geq 2) \).

Let me know if you'd like me to complete the calculations or have further questions!

Here are 5 related questions to deepen your understanding:

1. How would the probability change if the sample size increased from 8 to 10 adults?
2. What is the probability that exactly 4 adults use their smartphones in meetings or classes?
3. How does the complement rule simplify probability calculations in this context?
4. What if the probability of using smartphones in meetings or classes was 60% instead of 48%?
5. How would you approach finding the expected number of smartphone users in this scenario?

**Tip**: Always consider using the complement rule when calculating the probability of "at least" scenarios, as it can often simplify the calculations.

Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that at least 2 of them use their smartphones in meetings or classes.

Find the probability that at least 2 out of 8 adults use their smartphones in meetings or classes, given a 48% probability. This problem involves the binomial distribution and the complement rule to simplify calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation