To calculate $P(\text{not 9})$, we first need to determine the probability of spinning any number other than 9.

Step 1: Total outcomes

The spinner contains the numbers $5, 6, 7, 8,$ and $9$, which gives us a total of 5 outcomes.

Step 2: Favorable outcomes for "not 9"

The numbers that are not 9 are $5, 6, 7,$ and $8$, which means there are 4 favorable outcomes for spinning something other than 9.

Step 3: Calculate probability

The probability is calculated using the formula: $P(\text{not 9}) = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{4}{5}.$

Final Answer:

$P(\text{not 9}) = \frac{4}{5} \text{ or } 0.8.$

Would you like a more detailed explanation or visualization? 😊

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Here are 5 related questions to expand on this concept:

1. What is $P(9)$ for the same spinner?
2. If you spin the spinner twice, what is $P(\text{not 9 on both spins})$?
3. What is the probability of spinning a 5 or a 7 in one spin?
4. If the spinner were modified to include more numbers, how would this change $P(\text{not 9})$?
5. How would you calculate $P(\text{exactly one 9 in two spins})$?

Tip: Always double-check the total number of outcomes when working with probabilities to avoid errors!