Chapter 5.3, Problem 95E

To determine

To find: the probability that the student uses Myspace regularly.

Answer to Problem 95E

  $P\left(\text{My space/Facebook}\right)=49.41\%$

Explanation of Solution

Given:

A recent survey suggest that 85% of the college students have posted a profile on Facebook, 54% on Myspace regularly, and 42% do both.

Concept used:

Complement rule: $P\left(\text{not}A\right)=1-P\left(A\right)$

Definition conditional probability:

  $P\left(B/A\right)=\frac{P\left(A\text{ and}B\right)}{P\left(A\right)}$

Calculation:

  $\begin{array}{l}P\left(\text{Facebook}\right)=85\%=0.85\\ P\left(\text{My space}\right)=54\%=0.54\end{array}$

Complement rule:

  $P\left(\text{Facebook}\cap \text{My space}\right)=42\%$

  $\begin{array}{l}P\left(\text{not lost}\right)=1-P\left(\text{lost}\right)\\ =1-0.13=0.87\end{array}$

Definition conditional probability:

  $P\left(B/A\right)=\frac{P\left(A\text{ and}B\right)}{P\left(A\right)}$

Apply the definition conditional probability, thus obtained:

  $\begin{array}{l}P\left(\text{My space/Facebook}\right)=\frac{0.42}{0.85}=\frac{42}{85}\\ \approx 0.4941=49.41\%\end{array}$