If a coin is flipped 15 times what is the probability of getting exactly 10 heads
To find the probability of getting exactly 10 heads when a coin is flipped 15 times, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx) * (p^x) * (q^(n-x))
Where:
P(x) is the probability of getting exactly x successes,
n is the total number of trials,
x is the number of successful outcomes,
p is the probability of success on a single trial, and
q is the probability of failure on a single trial (q = 1 - p).
In this case, the number of trials (n) is 15, the number of successful outcomes (x) is 10, the probability of success on a single trial (p) is 0.5 (since there is an equal chance of getting heads or tails on a fair coin flip), and the probability of failure on a single trial (q) is also 0.5.
Therefore, substituting the given values into the binomial probability formula:
P(10) = (15C10) * (0.5^10) * (0.5^(15-10))
Calculating the binomial coefficient (15C10) = 3003, we get:
P(10) = 3003 * (0.5^10) * (0.5^5)
= 3003 * (0.0009765625) * (0.03125)
= 0.29296875
Thus, the probability of getting exactly 10 heads when a coin is flipped 15 times is approximately 0.29296875, or 29.3%.