To determine the probability of flipping a coin and getting tails four times in a row, we first need to understand how probability works for independent events like coin flips. A standard coin has two sides: heads (H) and tails (T), which means the probability of landing on tails in a single flip is 1 out of 2, or mathematically, P(T) = 1/2.
Since each flip of the coin is an independent event, the outcome of one flip does not affect the others. Therefore, to find the probability of multiple flips resulting in tails, we multiply the probability of tails for each flip together. This can be represented as:
P(Tails 4 times) = P(T) × P(T) × P(T) × P(T)
Substituting the probability of tails:
P(Tails 4 times) = (1/2) × (1/2) × (1/2) × (1/2)
Calculating this gives us:
P(Tails 4 times) = (1/2)^4 = 1/16
So, the probability of getting tails four times in a row when flipping a fair coin is 1/16, or equivalently, 6.25%. To put it another way, if you were to flip a coin many times, you could expect to get four tails in a row approximately once every 16 attempts. This illustrates the nature of probability, particularly with independent events like coin flipping.