X Consider a coin with the probability of head p = 0.3. Provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads. (b Repeat the above part for a fair coin with the probability of head p = 0.5, i.e., provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads. (c) If a third party mixes the two coins, how can you distinguish between the two coins?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Fair vs Unfair Coin:

**a.** Consider a coin with the probability of head \( p = 0.3 \). Provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads.

**b.** Repeat the above part for a fair coin with the probability of head \( p = 0.5 \), i.e., provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads.

**c.** If a third party mixes the two coins, how can you distinguish between the two coins?
Transcribed Image Text:### Fair vs Unfair Coin: **a.** Consider a coin with the probability of head \( p = 0.3 \). Provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads. **b.** Repeat the above part for a fair coin with the probability of head \( p = 0.5 \), i.e., provide an estimate for the probability that after 1000 flipping of this coin we observe between 250 and 350 heads. **c.** If a third party mixes the two coins, how can you distinguish between the two coins?
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