Question

An anti-aircraft gun can fire four shots at a time. Suppose that we are interested in whether each shot has hit the enemy aircraft or not. How many elements does the sample space of this experiment have?

Answer 1

The sample space for the experiment of firing the anti-aircraft gun has
`\(2^4 = 16\)` elements.

The sample space of an experiment is the set of all possible outcomes of that experiment. In this case, the experiment is firing the anti-aircraft gun, and the outcomes are whether each shot hits the enemy aircraft or not.

For each shot, there are two possible outcomes: either it hits the enemy aircraft (success) or it does not hit the enemy aircraft (failure).

Since there are four shots fired independently, the total number of outcomes for the experiment is the product of the number of outcomes for each shot. Therefore, the sample space for the experiment of firing the anti-aircraft gun has
`\(2^4 = 16\)` elements.

Each element in the sample space represents a different combination of hits and misses for the four shots.