4. A friend of yours who took Stat 241 last year is extremely bored and so begin

Question

4. A friend of yours who took Stat 241 last year is extremely bored and so begins to flip a coin and record the outcomes on a sheet of paper. When he gets to 1000 flips he muses aloud, "Hmmm. I've only got 479 heads. That's 21 below what I'd expect. But I remember the Law of Averages tells me that I'll get closer and closer to the expected value the more times I flip this thing. I'll bet if I keep going until I make 10,000 flips I'll probably be fewer than 21 heads away from my expected 5,000". Is your friend right? If not, why not?

Explanation / Answer

Yes, your friend is correct.

This is because the probabiltiy of getting head on any flip of coin is 0.5 and the expected number of heads are 5000. As per the law of average, there are chances that the number of heads we were lagging will be covered in subsequent trials.

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