What is the probability that both heads and tails occur?

Question

involving flipping a fair coin. Assume that the coin is flipped 3 times.
What is the probability that both heads and tails occur?

Answer 1

For probability questions like this, involving coins, sometimes it's helpful to list out all possible combinations. For 3 flips of a coin, we have the following possible outcomes:

 

HHH   TTT

HHT    TTH

HTH    THT

HTT    THH

 

So now you can easily pick the outcomes and take that over how many outcomes are possible. From the above list, only 2 of the 8 DO NOT involve both a heads AND a tails (HHH or TTT), or, 6/8 involve both. The probability it 3/4 or 75%