A coin is flipped 15 times.
What is the probability P(X=10)
To find the probability P(X=10), we need to use the binomial distribution formula:
P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k))
Where:
- n is the number of trials (15 in this case)
- k is the number of successful outcomes (10 in this case)
- p is the probability of success on a single trial (0.5 for a fair coin flip)
Using these values, we can calculate the probability P(X=10):
P(X=10) = (15 choose 10) * (0.5^10) * ((1-0.5)^(15-10))
= (3003) * (0.5^10) * (0.5^5)
= 3003 * 0.0009765625 * 0.03125
≈ 0.09375
Therefore, the probability P(X=10) is approximately 0.09375 or 9.375%.