# probability and statistics

**Question description**

In a particular game show, a contestant is given the option of selecting from three mystery boxes, one of which contain a prize. The contestant is given the opportunity to win up to 5 prizes by repeating thsi same procedure. If the contestant wins all 5 prizes, he/she gets a bonus round in which to choose from 10 boxes. one of which contains $1000

1. what is the probability that the contestant walks away empty handed?

2. What is the probability that the contestant wins exactly 4 prizes

3. What is the probability that the contestant wins no less than 2 prizes

4. What is the contestants expected number of prizes (regular rounds only) ? Interpret this result

5. What is the overall probability that the contestant wins $1000

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