Final answer:
The probability of getting exactly 2 heads when flipping a fair coin 6 times is 0.09375, or 9.375%.
Step-by-step explanation:
To find the probability of getting exactly 2 heads when flipping a fair coin 6 times, we can use the binomial probability formula.
Using the binomial probability formula: P(x) = (nCx) * p^x * q^(n-x)
Where:
- P(x) is the probability of getting exactly x successes (in this case, heads)
- n is the number of trials (flips)
- x is the number of successes we want (2 heads)
- p is the probability of success (getting a head, which is 0.5 for a fair coin)
- q is the probability of failure (getting a tail, which is also 0.5 for a fair coin)
Plugging in the values: P(2) = (6C2) * (0.5)^2 * (0.5)^(6-2)
Simplifying:
- Using combinations: P(2) = (6! / (2! * (6-2)!)) * (0.5)^2 * (0.5)^(6-2)
- Calculating: P(2) = 15 * 0.25 * 0.25 = 0.09375
Therefore, the probability of getting exactly 2 heads when flipping a fair coin 6 times is 0.09375, or 9.375%.