Question

A fair coin is flipped four times. What is the probability of observing at least one tail?

Answer 1

2/4

Answer 2

theoretical probability - p (event) = # of favorable outcomes/# of outcomes in the sample space

Answer 3

Unfortunately the accepted answer is incorrect.

We can solve this using the Choose function. Let n = 4 (number of flips), k=1 (number of tails).

To find the odds of exactly one flip in four being tails, Choose(4,2) * P^k(1-P)^(n-k)

Here, P is the probability of the event occurring in a single instance (which is 50%, k and n are already defined), thus.. Choose(4,2) * 0.5^1 * (1-0.5)^(4-1) = 25% chance (0.25)

However, since you are looking for the event to occurring *at least* once, we must also calculate the probabilities of the tail landing 2, 3 or 4 times. We simply change k to equal 2,3,4 respectively in the three separate calculations. We then sum these probabilities together to arrive at the correct answer, which is 93.75%.

Answer 4

In other words, the probability of there only being heads is 6.25%