To find the probability of getting exactly 2 tails when tossing a coin 5 times, we can use the binomial probability formula. The binomial formula is expressed as:
P(X = k) = C(n, k) * p^k * (1 – p)^(n – k)
Where:
- P(X = k) is the probability of getting exactly k successes (in our case, tails).
- C(n, k) is the number of combinations of n items taken k at a time, calculated as n! / (k! * (n – k)!).
- p is the probability of success on a single trial (0.5 for a fair coin).
- n is the number of trials (5 tosses).
- k is the number of successes we want (2 tails).
In our scenario:
- n = 5
- k = 2
- p = 0.5
First, we calculate C(5, 2):
C(5, 2) = 5! / (2! * (5 – 2)!) = (5 * 4) / (2 * 1) = 10
Next, we calculate the probability:
P(X = 2) = C(5, 2) * (0.5)^2 * (0.5)^(5 – 2)
P(X = 2) = 10 * (0.5)^2 * (0.5)^3
P(X = 2) = 10 * 0.25 * 0.125
P(X = 2) = 10 * 0.03125 = 0.3125
So, the probability of getting exactly 2 tails when tossing a coin 5 times is 0.3125, or 31.25%.