Gerrit attempted 54 free throws and made 27. What is the probability in a two attempt free - throw situation that he will make 0 points ? 1point ? 2 points ?

prob(hit) = 27/54 = 1/2

prob( miss) = 1/2

prob (no points)
= prob(miss, miss) = (1/2)(1/2) = 1/4
prob( 1 point)
= prob(HM) + Prob(MH) = 2(1/4) = 1/2

prob(2 points) ]= prob (HH) = 1/4

(notice 1/4 + 1/2 + 1/4 = 1 , as expected)

To find the probability, we need to know the total number of possible outcomes and the number of desired outcomes.

In this case, Gerrit attempted 54 free throws, which means each free throw can have two outcomes: either he makes the shot (1 point) or misses the shot (0 points). So, for each attempt, there are two possible outcomes.

We can calculate the total number of possible outcomes by multiplying the number of possibilities for each attempt. In this case, since we have two attempts, we would multiply 2 by itself: 2 * 2 = 4.

Now let's calculate the probability of each desired outcome:

1. Probability of making 0 points (miss both attempts): As mentioned earlier, each attempt has two possible outcomes (make or miss), so both attempts together would have 2 * 2 = 4 possible outcomes. Since we want to find the probability of making 0 points, which is only 1 desired outcome, the probability would be 1/4, or 0.25.

2. Probability of making 1 point: There are two scenarios where Gerrit can make 1 point - either he makes the first attempt and misses the second, or he misses the first and makes the second. Each scenario has a probability of 1/4, so the total probability of making 1 point is 1/4 + 1/4 = 2/4, which simplifies to 1/2 or 0.5.

3. Probability of making 2 points: Gerrit can only make 2 points if he makes both attempts. As mentioned earlier, the probability of making a single attempt is 1/4, so the probability of making both attempts would be (1/4) * (1/4) = 1/16.

Therefore, the probabilities are as follows:
- Probability of making 0 points: 0.25 or 25%
- Probability of making 1 point: 0.5 or 50%
- Probability of making 2 points: 0.0625 or 6.25%