10. Whenever Hannah turns on her cell phone, it randomly shows a background image from a group of 6 images Hannah has selected. Of the 6 images Hannah has selected,
- exactly 2 are of her friends,
- exactly 3 are of her family members, and
- exactly 1 is of her pet dog.
What is the probability that the cell phone shows an image other than the pet dog the next time Hannah turns on her cell phone?

Answer

Expert–verified

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Answer

\(P(\text{not pet dog}) = \frac{5}{6}\)

Steps

Step 1 ：\(P(\text{not pet dog}) = \frac{\text{number of non-pet dog images}}{\text{total number of images}}\)

Step 2 ：\(P(\text{not pet dog}) = \frac{2 + 3}{6}\)

Step 3 ：\(P(\text{not pet dog}) = \frac{5}{6}\)