John has three chances of throwing and hitting the target to win the prize. One hit wins John the prize. What is the probability of John not winning if any given throw has a 80% chance of hitting the target?
The probability of hitting the target on any given throw is 80%, so the probability of not hitting the target on any given throw is 20%.
Since John has three chances to hit the target, the probability of not winning (i.e. not hitting the target on all three throws) is:
0.2 x 0.2 x 0.2 = 0.008
Therefore, the probability of John not winning is 0.008 or 0.8%.