To find the probability of getting exactly 2 tails when flipping a fair coin 7 times, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- C(n, k) is the number of combinations of n items taken k at a time,
- p is the probability of success (getting tails in this case),
- n is the number of trials (coin flips),
- k is the number of successes (tails).
In this scenario:
- n = 7 (the number of flips),
- k = 2 (the number of tails),
- p = 0.5 (the probability of getting tails on a flip).
First, we calculate C(7, 2):
C(7, 2) = 7! / (2!(7-2)!) = (7*6) / (2*1) = 21
Next, we can plug the values into the binomial formula:
P(X = 2) = C(7, 2) * (0.5)^2 * (0.5)^(7-2)
P(X = 2) = 21 * (0.5)^2 * (0.5)^5
P(X = 2) = 21 * (0.5)^7
P(X = 2) = 21 / 128
Therefore, the probability of getting exactly 2 tails when flipping a fair coin 7 times is:
21/128 or approximately 0.1641 (16.41%).