A coin is flipped 15 times.
What is the probability of getting more than 12 heads
To find the probability of getting more than 12 heads, we need to calculate the probability of getting 13, 14, or 15 heads.
The probability of getting a head on a single flip of a fair coin is 0.5 since there are two equally likely outcomes (head or tail) and one of them is a head.
Using the binomial probability formula, the probability of getting exactly x successes (heads) in n trials (flips) can be calculated as:
P(x) = C(n, x) * p^x * q^(n-x)
Where C(n, x) represents the number of combinations of n items taken x at a time, p is the probability of success (getting a head), q is the probability of failure (getting a tail), and n is the number of trials (flips).
For getting exactly 13 heads in 15 flips, the probability is:
P(13) = C(15, 13) * (0.5)^13 * (0.5)^(15-13) = 105 * (0.5)^15
Using a similar formula, the probability of getting exactly 14 heads in 15 flips is:
P(14) = C(15, 14) * (0.5)^14 * (0.5)^(15-14) = 15 * (0.5)^15
Lastly, the probability of getting exactly 15 heads in 15 flips is:
P(15) = C(15, 15) * (0.5)^15 * (0.5)^(15-15) = 1 * (0.5)^15
To find the probability of getting more than 12 heads, we sum up the probabilities of getting 13, 14, and 15 heads:
P(more than 12 heads) = P(13) + P(14) + P(15) = 105 * (0.5)^15 + 15 * (0.5)^15 + (0.5)^15
Calculating this value, we get:
P(more than 12 heads) ≈ 0.00384
So, the probability of getting more than 12 heads when flipping a coin 15 times is approximately 0.00384, or 0.384%.