Final answer:
The probability of a flipped coin landing on heads four times out of six trials is approximately 0.234375 or 23.44%.
Step-by-step explanation:
The probability of a flipped coin landing on heads four times out of six trials can be calculated using the binomial probability formula.
The formula for calculating the probability of getting exactly k successes (in this case, heads) in n trials is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- C(n, k) is the number of combinations of n objects taken k at a time.
- p is the probability of success (in this case, heads).
- n is the total number of trials (in this case, 6).
In this case, we want to find the probability of getting exactly 4 heads, so k = 4.
Since the probability of landing on heads is 0.5 for a fair coin, p = 0.5.
Using the formula:
P(X = 4) = C(6, 4) * (0.5)^4 * (1-0.5)^(6-4)
Simplifying the equation:
P(X = 4) = (15) * (0.5)^4 * (0.5)^2
P(X = 4) = 0.234375
Therefore, the probability of a flipped coin landing on heads four times out of six trials is approximately 0.234375 or 23.44%.