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A coin is flipped 8 times. Find the probability of the event: exactly 8 heads.

Options:
a. 0.004
b. 1
c. 0.0625
d. 0.109

User Tathiana
by
8.5k points

1 Answer

2 votes

Final answer:

To find the probability of getting exactly 8 heads when flipping a coin 8 times, we can use the binomial probability formula. The probability is approximately 0.0039.

Step-by-step explanation:

To find the probability of getting exactly 8 heads when flipping a coin 8 times, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * q^(n-k)

Where P(X = k) is the probability of getting exactly k successes, n is the total number of trials, k is the number of successes, p is the probability of success on a single trial, and q is the probability of failure on a single trial.

In this case, n = 8, k = 8, p = 0.5, and q = 0.5.

Plugging these values into the formula:

P(X = 8) = C(8, 8) * 0.5^8 * 0.5^(8-8) = 1 * 0.5^8 * 0.5^0 = 0.5^8 = 0.00390625

So the probability of getting exactly 8 heads when flipping a coin 8 times is approximately 0.0039, which is option a. 0.004.

User Nicholas Patton
by
7.9k points
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