The Pew Research Center has found that 86% of people 18 through 29 years old are social media users.
What is the probability that you have to ask 10 people in this age group to find one that is not a social media user?
What is the probability that you have to ask 20 people in this age group to find one that is not a social media user?
What is the probability you must ask at most 5 people in this age group to find one that is not a social media user?
prob(user) = .86
prob(not user) = .14
prob(of 10, 1 is not a user)
= C(10,1)(.14)^1 (.86)^9 = appr .36
do the others in the same way
To answer these questions, we need to use the concept of complementary probability.
The probability of finding a person who is not a social media user in a random selection can be calculated by subtracting the probability of finding a social media user from 1.
Given that 86% of people in the age group 18-29 are social media users, the probability of finding a social media user is 0.86.
Let's calculate the probabilities for each question.
1. Probability of asking 10 people to find one who is not a social media user:
To calculate this probability, we need to find the probability of not finding a non-social media user in 10 attempts.
The probability of not finding a non-social media user in one attempt is 0.86.
The probability of not finding a non-social media user in 10 attempts is calculated as:
P(not finding a non-social media user in 10 attempts) = (0.86)^10
So, the probability of finding at least one non-social media user when asking 10 people is:
P(asking 10 people to find one non-social media user) = 1 - (0.86)^10
2. Probability of asking 20 people to find one who is not a social media user:
Similar to the previous question, we need to calculate the probability of not finding a non-social media user in 20 attempts.
The probability of not finding a non-social media user in one attempt is 0.86.
The probability of not finding a non-social media user in 20 attempts is:
P(not finding a non-social media user in 20 attempts) = (0.86)^20
So, the probability of finding at least one non-social media user when asking 20 people is:
P(asking 20 people to find one non-social media user) = 1 - (0.86)^20
3. Probability of asking at most 5 people to find one who is not a social media user:
To calculate this probability, we need to find the cumulative probability of finding a non-social media user in 1, 2, 3, 4, or 5 attempts.
The probability of finding a non-social media user in one attempt is 1 - 0.86 = 0.14.
So, the probability of finding a non-social media user in at most 5 attempts is:
P(finding a non-social media user in at most 5 attempts) = 1 - (0.86)^5
Note: These calculations are based on the assumption that each person in the age group is independent, and the probability of being a social media user is consistent across the entire population.