Question

question 6
a 2014 survey suggests that 71% of u.s. teenagers use facebook, 33% use twitter, and 15% do both. suppose we select a u.s. teenager at random and learn that the student uses facebook. find the probability that the student uses twitter.

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that a teenager uses Twitter and \(B\) be the event that a teenager uses Facebook.

Step2: Identify the values

We are given that \(P(B) = 0.71\) (probability of using Facebook), \(P(A\cap B)=0.15\) (probability of using both Facebook and Twitter).

Step3: Substitute the values into the formula

Substitute \(P(A\cap B) = 0.15\) and \(P(B)=0.71\) into the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). So \(P(A|B)=\frac{0.15}{0.71}\approx0.2113\)

Answer:

The probability that the student uses Twitter given that the student uses Facebook is approximately \(0.2113\)