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#probability
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Suppose afair coin is flipped 6 times and it is recorded whether the coin lands heads or tails what is the probability of getting 4 heat?

Dec 4, 2023

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Dec 4, 2023

To find the probability of getting 4 heads when flipping a fair coin 6 times, we can use the binomial probability formula.

The formula for the probability of getting exactly k successes in n trials, where the probability of success in each trial is p, is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In this case, n = 6 (number of trials), k = 4 (number of successes), and p = 0.5 (probability of getting heads in each trial).

Plugging in these values into the formula, we get:

P(X = 4) = (6 choose 4) * (0.5)^4 * (1-0.5)^(6-4)

Calculating the values:

(6 choose 4) = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15

(0.5)^4 = 0.0625

(1-0.5)^(6-4) = 0.25

Now, substituting these values into the formula:

P(X = 4) = 15 * 0.0625 * 0.25 = 0.234375

Therefore, the probability of getting 4 heads when flipping a fair coin 6 times is approximately 0.234375, or 23.44%.

The formula for the probability of getting exactly k successes in n trials, where the probability of success in each trial is p, is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In this case, n = 6 (number of trials), k = 4 (number of successes), and p = 0.5 (probability of getting heads in each trial).

Plugging in these values into the formula, we get:

P(X = 4) = (6 choose 4) * (0.5)^4 * (1-0.5)^(6-4)

Calculating the values:

(6 choose 4) = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15

(0.5)^4 = 0.0625

(1-0.5)^(6-4) = 0.25

Now, substituting these values into the formula:

P(X = 4) = 15 * 0.0625 * 0.25 = 0.234375

Therefore, the probability of getting 4 heads when flipping a fair coin 6 times is approximately 0.234375, or 23.44%.