1,000,000 Coin Flips

Probability Level 3

Suppose that we flip 1 , 000 , 000 1,000,000 fair coins and obtain X X heads. Which event is more likely?

Source: Aha! Solutions by Martin Erickson

X = 500,000 0 ≤ X ≤ 495,000

Jane Maleza by Jane Maleza , 17, Philippines

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1 solution

Probability [ x = 500000 , x ∼ ∼ BinomialDistribution [ 1000000 , 1 2 ] ] > Probability [ 0 < x < 495000 , x ∼ ∼ BinomialDistribution [ 1000000 , 1 2 ] ] ⇒ True \text{Probability}\left[x=500000,x\overset{\sim}{\sim}\text{BinomialDistribution}\left[1000000,\frac{1}{2}\right]\right]> \\ \text{Probability}\left[0<x<495000,x\overset{\sim}{\sim}\text{BinomialDistribution}\left[1000000,\frac{1}{2}\right]\right] \Rightarrow \\ \text{True}

In fact the 495000 could be increased to 498422 and it would still be true.

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