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2 Answers

Best answer
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2 votes

Assuming we need exactly 50 heads

100C50 1/250 1/250 ≈ 0.1

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The probability of getting exactly k heads in n tosses of a fair coin is given by the binomial distribution formula:

P(k heads in n tosses) = (n choose k) * p^k * (1-p)^(n-k)

where p is the probability of getting a head on any one toss of the coin.

In this case, we want to find the probability of getting 50 heads in 100 tosses of a fair coin, so we have:

P(50 heads in 100 tosses) = (100 choose 50) * 0.5^50 * 0.5^50

= (100 choose 50) * 0.5^100

Using Stirling's approximation for factorials, we can approximate (100 choose 50) as:

(100 choose 50) ≈ (2pi50)^(-1/2) * (100/50)^50

Plugging this into the expression above, we get:

P(50 heads in 100 tosses) ≈ (2pi50)^(-1/2) * (100/50)^50 * 0.5^100

≈ 0.0796

So the closest answer choice is 0.1.

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