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 70% chance of hitting the target?
Since each throw is independent of the others, the probability of not hitting the target on any given throw is 1 - 0.7 = 0.3.
Since John has three chances to hit the target, the probability of not winning the prize on all three throws is 0.3 * 0.3 * 0.3 = 0.027.
Therefore, the probability of John not winning the prize is 0.027, or 2.7%.