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7-58.

Earl (from Chapter 6) still hates to wash the dishes and take out the garbage. He found his own weighted coin, one that would randomly land on heads $30\%$ of the time. He will flip a coin once for each chore and will perform the chore if the coin lands on heads.

1. What is the probability that Earl will get out of doing both chores?

Create a model that illustrates all possible outcomes.

Tree Diagram. Flip 1: Two branches with the probability of 0.3, wash dishes, and 0.7, no chore. Flip 2: Wash Dishes splits into two branches Take out the Garbage, ( 0.3 ), and No chore, ( 0.7). No chore splits into two branches , take out the garbage, ( 0.3 ) and no chore, ( 0.7).

The probability that Earl gets out of both chores is 0.7 times 0.7. Refer to this model when solving.

2. What is the probability that Earl will have to take out the garbage, but will not need to wash the dishes?

The probability that Earl gets out of both chores is 0.7 times 0.3. Refer to this model when solving.