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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?
Anonymous
Dec 4, 2023
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#probability
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?
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Dec 4, 2023
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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%.
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