  ### Home > INT3 > Chapter 6 > Lesson 6.2.4 > Problem6-66

6-66.

Riley updates her phone to play a song when either of her parents call. The ringtone can be a song from a playlist of six songs: one of the songs is her parents’ wedding song, two of them are reggae songs since her dad loves reggae, and three of them are jazz music since her mom loves jazz.

1. Create an area model to represent this situation. Assume that her parents are equally likely to call.

 Jazz$\frac{1}{2}$ Reggae$\frac{1}{3}$ Wedding$\frac{1}{6}$ Mom$\frac{1}{2}$ Dad$\frac{1}{2}$
2. What is the probability that the song will not be her parents’ wedding song?

What is the probability of the song being jazz or reggae?

3. When the wedding song plays for mom, or a jazz song plays for dad, Riley’s phone shows a smiling emoticon. What is the probability her phone will show a smiling emoticon?

$\frac{1}{2}\cdot \frac{1}{6}+\frac{1}{2}\cdot \frac{1}{2}\approx33.3\%$

4. Given that Riley’s phone displayed a smiling emoticon, what is the conditional probability her dad called?

$\frac{P(\text{dad and emoticon})}{P(\text{emoticon})} = ?$

$=\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{3}{4}=75\%$