To determine how many times the spinner would land on an even number in 600 spins, given that the probability of landing on an even number is [tex]\(\frac{5}{10}\)[/tex], we can follow these steps:
1. Understand the probability: The probability of the spinner landing on an even number is given as [tex]\(\frac{5}{10}\)[/tex]. This means that out of every 10 spins, the spinner is expected to land on an even number 5 times.
2. Set up the calculation: To find the expected number of even number spins out of 600 total spins, you multiply the total number of spins by the probability of landing on an even number:
[tex]\[
\frac{5}{10} \times \frac{600}{1}
\][/tex]
3. Simplify the fraction: The probability [tex]\(\frac{5}{10}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex]. So, we can rewrite the equation as:
[tex]\[
\frac{1}{2} \times 600
\][/tex]
4. Perform the multiplication: Multiply [tex]\(\frac{1}{2}\)[/tex] by 600:
[tex]\[
\frac{1}{2} \times 600 = 300
\][/tex]
Therefore, the expected number of times the spinner would land on an even number out of 600 spins is [tex]\(300\)[/tex].
