Compound Probability of Independent Events

1. Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home.

If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?

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2. If you roll two fair six-sided dice, what is the probability that the sum is $9$ or higher?

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3. You're at a clothing store that dyes your clothes while you wait. You get to pick from $4$ pieces of clothing (shirt, pants, socks, or hat) and $3$ colors (purple, blue, or orange).

If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?

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4. If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?

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