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6-39.

Kendra has programmed her cell phone to randomly show one of six photos when she turns it on. Two of the photos are of her parents, one is of her niece, and three are of her boyfriend, Bruce. Today she will need to turn her phone on twice: once before school and again after school.

1. Choose a model (such as a tree diagram or generic area model) to represent this situation.

See possible area model below.

 top edge left parents$\frac{1}{3}$ top edge middle niece$\frac{1}{6}$ top edge left boyfriend$\frac{1}{2}$ left edge topparents$\frac{1}{3}$ interior top left$\space$$\frac{1}{9}$$\space$ interior top middle$\space$$\frac{1}{18}$$\space$ interior top right$\space$$\frac{1}{6}$$\space$ left edge middleniece$\frac{1}{6}$ interior middle left$\space$$\frac{1}{18}$$\space$ interior middle middle$\space$$\frac{1}{36}$$\space$ interior middle right$\space$$\frac{1}{12}$$\space$ left edge bottomboyfriend$\frac{1}{2}$ interior bottom left$\space$$\frac{1}{6}$$\space$ interior bottom middle$\space$$\frac{1}{12}$$\space$ interior bottom right$\space$$\frac{1}{4}$$\space$
2. What is the probability that both photos will be of her boyfriend?

Use the area model in hint (a) to determine the probability.

${\frac{1}{4}}$

3. What is the probability that neither photo will be of her niece?

Add up all the combinations that do not include a photo of Kendra's niece.