1. You toss a fair coin four times in a row and it lands on tails all four times. What is the probability that your next coin toss will be tails?

2. A carnie at the fair has hidden a gold ring under one of three cups, marked A, B, and C. He lets you name one cup as your choice. You pick cup A. He then lifts cup C, showing you that it's empty, and allows you to choose again. What are the odds that the ring is under cup B?

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This is a two part question:

1. You toss a fair coin four times in a row and it lands on tails all four times. What is the probability that your next coin toss will be tails?

2. A carnie at the fair has hidden a gold ring under one of three cups, marked A, B, and C. He lets you name one cup as your choice. You pick cup A. He then lifts cup C, showing you that it's empty, and allows you to choose again. What are the odds that the ring is under cup B?

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