To find the probability that Julian will make at least one three-pointer in a game, we need to calculate the probability of the complementary event (making zero three-pointers) and then subtract that probability from 1.

Step-by-step process:

1. The complementary event is making 0 three-pointers.

   • The probability of making 0 three-pointers is given as 0.12.

2. At least one three-pointer means that the number of three-pointers made is greater than or equal to 1. This is the complement of making 0 three-pointers.

3. The formula for finding the probability of an event happening at least once is: $P(\text{at least 1}) = 1 - P(\text{making 0})$

4. Substituting the values we know: $P(\text{at least 1}) = 1 - 0.12 = 0.88$

Final Answer:

The probability that Julian will make at least one three-pointer in a game is 0.88.

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Would you like me to explain this further or break down any other part of it? Also, here are 5 related questions that could help you dive deeper into probability:

1. What is the probability that Julian will make exactly 3 three-pointers in a game?
2. How would you calculate the probability of making 4 or more three-pointers in a game?
3. If the probability of making 0, 1, or 2 three-pointers are given, how would you calculate the probability of making 3 or more three-pointers?
4. How does the sum of all individual probabilities in a probability distribution relate to the total probability?
5. How would you interpret the concept of "complementary events" in probability?

Tip: When working with probability distributions, remember that the sum of the probabilities of all possible outcomes must equal 1. This can help you check if your calculations are correct.