Question

According to the Pew Research Group, 81% of teens use social media networks. Suppose five teens are randomly selected. What is the probability that all 5 use social media networks? Round your answer to 4 decimal places.

Options:
A. 0.3277
B. 0.3278
C. 0.3287
D. 0.3288

Answer 1

The probability that all 5 randomly selected teens use social media networks is found by multiplying the probability (0.81) five times. After calculating, the result is 0.3487, but this answer does not match any of the provided options, indicating a potential error in the options.

Step-by-step explanation:

The probability that all 5 randomly selected teens use social media networks, given that 81% of teens use social media networks, can be calculated using the multiplication rule for independent events. Since we are considering the same probability (81% or 0.81) for each teen independently, this is a binomial situation where we only want the probability of 5 successes out of 5 attempts.

Here is how we calculate it step-by-step:

1. Express the given percentage as a decimal: 81% = 0.81
2. Multiply the probability together five times because we have five independent teens: 0.81 * 0.81 * 0.81 * 0.81 * 0.81
3. Calculate the result of the multiplication: 0.81^5 = 0.3486
4. Round the answer to four decimal places: 0.3486 ≈ 0.3487 (None of the options given are correct)

Therefore, the probability that all 5 teens use social media networks is approximately 0.3487, when rounded to four decimal places.