To determine the probability that the first number on the game spinner is a 3 and the second number is a 6, we will break down the problem into the following steps:
1. Count the total number of possible outcomes per spin:
The game spinner is divided into 9 regions, each numbered from 1 to 9. Therefore, the total number of possible outcomes for one spin is 9.
2. Find the probability of spinning a 3 on the first spin:
Since there is only one way to spin a 3 out of 9 possible outcomes, the probability of spinning a 3 is:
[tex]\[
\text{Probability of spinning a 3} = \frac{1}{9}
\][/tex]
3. Find the probability of spinning a 6 on the second spin:
Similarly, since there is only one way to spin a 6 out of the 9 possible outcomes, the probability of spinning a 6 is:
[tex]\[
\text{Probability of spinning a 6} = \frac{1}{9}
\][/tex]
4. Calculate the combined probability of both events occurring:
Since the spins are independent events, the combined probability of the first outcome being a 3 and the second outcome being a 6 is the product of the two probabilities:
[tex]\[
\text{Combined probability} = \left( \frac{1}{9} \right) \times \left( \frac{1}{9} \right) = \frac{1}{81}
\][/tex]
Therefore, the probability that the first number is a 3 and the second is a 6 is:
[tex]\[
\boxed{\frac{1}{81}}
\][/tex]
