To ensure the table represents a probability distribution, the sum of all probabilities must equal 1. Here’s how to find the missing probability:

1. Sum the given probabilities: $0.2 + 0.2 + 0.3 = 0.7$

2. Since the total probability must equal 1, the missing probability $P(8)$ can be found by subtracting the sum of the given probabilities from 1: $P(8) = 1 - 0.7 = 0.3$

So, the missing probability for $x = 8$ is 0.3.

Would you like a further breakdown of this concept or have any questions?

Here are some related questions to explore:

1. How do we know if a table represents a valid probability distribution?
2. What are the properties of probability distributions?
3. How can we verify if a set of probabilities meets distribution requirements?
4. What is the probability of each individual outcome in this scenario?
5. How do probability distributions apply in real-world situations?

Tip: In any probability distribution, make sure the probabilities of all possible outcomes sum to 1 to verify its validity.