flip a fair coin 10000 times. approximate the probability that difference number of heads and tails is atleast 100
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Answer:
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If you flipped a coin 10,000 times, how many times would you expect to get heads?
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Martin Jansche
Answered November 18, 2019
Most of the other answers interpret your usage of “expect” as asking for the expected value and give you a correct point answer of 5000. And indeed you will get about 5000 heads in 10,000 iid fair coin flips.
However, you’ll get exactly 5000 heads only about 0.8% of the time if you repeat that process indefinitely. The other times you get a total number of heads which is close to 5000. You may now reasonably ask: how close, and how often?
Another way to answer what you should “expect” to see is via an interval. For example, you can expect to see 5000±129 heads about 99% of the time in the long
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Nupur Bhosale
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David Marilley
Answered February 29, 2020
A fair coin flipped 10000 times will have a likely interval of outcomes. 95% of the time you should be within 1.96sqrt(2500) of 5000, which is the single most likely result. But if 4997, 4998, 4999, 5001, 5002 and 5003 gang up on 5000, then 5000 does not seem so likely. So “most" of the time we will be less than 100 heads above or below 5000. YES 100! The exact probability for {4901, 4902, 4903,…,5097,5098,5099} turns out to be .9534+. If we delete 4901 and 5099 from our “usual" interval, we get .9523-. If we delete 4902 and 5098, we get .9488+. Also note that 1.96×50 = 98. So 5000 give or take 98 is a shade over 95% in probability. 5000? You get that with probability. 007979, or less than 1% of the time.
Answer:
The probability that the difference between the number of heads and number of tails is at most 100 is P=0.84375.
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