you play a game using the spinner shown. find the probability that you get an even number on your first spin…

Explanation:

Step1: Calculate probability of first - spin

There are 8 numbers on the spinner. The even numbers are 2, 4, 8, so there are 3 even numbers. The probability of getting an even number on the first spin, $P(\text{even}_1)=\frac{3}{8}$.

Step2: Calculate probability of second - spin

The odd numbers are 1, 3, 5, 7, 9, so there are 5 odd numbers. The probability of getting an odd number on the second spin, $P(\text{odd}_2)=\frac{5}{8}$.

Step3: Calculate combined probability

Since the two spins are independent events, the probability of getting an even number on the first spin and an odd number on the second spin is $P = P(\text{even}_1)\times P(\text{odd}_2)$. Substitute the values: $P=\frac{3}{8}\times\frac{5}{8}=\frac{15}{64}$.

Step4: Convert to percentage

To convert $\frac{15}{64}$ to a percentage, we calculate $\frac{15}{64}\times100%=\frac{1500}{64}% = 23.4375%$.

Answer:

$23.4375$