A shooting game has 10 targets. The player has 10 arrows. In order to win the game, the player must shoot all 10 targets. What is the probability of shooting all 10 targets?
what is the probability of one arrow hitting one target?
To calculate the probability of shooting all 10 targets, we need to know the total number of possible outcomes and the number of successful outcomes.
In this case, the number of possible outcomes refers to all the possible ways the player can shoot the 10 targets. Each arrow can hit any target, so there are 10 choices for each arrow. Since there are 10 arrows in total, we have a total of 10 x 10 x 10 x... (10 times), or 10^10 possible outcomes.
The number of successful outcomes refers to the specific way in which all 10 targets are hit. Since the player must hit all the targets, there is only one successful outcome.
Now we can calculate the probability of shooting all 10 targets by dividing the number of successful outcomes by the number of possible outcomes:
Probability = Number of Successful Outcomes / Number of Possible Outcomes = 1 / (10^10)
So the probability of shooting all 10 targets in this game is 1 in 10^10, or 1 divided by 10 billion.