Coin Tossing Probability

Today, I want to talk about coin toss probability.

Please imagine that you toss 2000 coins.

Each coin will fall and rest with either side face up "heads" or "tails" with equal probability.

Well then, what is the probability that at least 1100 heads appear?

When I saw this problem for the first time, I thought intuitively the answer is around a few percent.

However, the actual answer is around 0.0004 percent, and it can be derived easily from a normal distribution.

This fact implies strong convergence of the probability.

I wondered the result for a while such as when I'm faced with a paradox, but people with probabilistic sense will understand without much resistance.

• Coin Tossing Probability
• This sentence is perfect! No correction needed!

• Today, I want to talk about coin toss probability.
• This sentence is perfect! No correction needed!

• Please imagine that you toss 2000 coins.
• This sentence is perfect! No correction needed!

• Each coin will fall and rest with either side face up "heads" or "tails" with equal probability.
• Each coin will fall and rest with either side face up "heads" or "tails" with equal probability.

  This sentence is good, but I think it may sound better as: Each coin will land with either the "heads" or the "tails" face up, both having an equal probability.

• Well then, what is the probability that at least 1100 heads appear?
• Well then, what is the probability that at least 1100 heads appear?

  This sentence is also good, but I suggest using "would be" instead of "is."

• When I saw this problem for the first time, I thought intuitively the answer is around a few percent.
• When I saw this problem for the first time, I intuitively thought the answer would be around a few percent.

  In this case I would use "would be" since the sentence structure shows you are uncertain. (ex. "I thought it would be 5, but it is 6.")

• However, the actual answer is around 0.0004 percent, and it can be derived easily from a normal distribution.
• This sentence is perfect! No correction needed!

• This fact implies strong convergence of the probability.
• This sentence is perfect! No correction needed!

• I wondered the result for a while such as when I'm faced with a paradox, but people with probabilistic sense will understand without much resistance.
• I wondered about the result for a while such as like when I'm faced with a paradox, but people with probabilistic sense will understand without much resistance.