Question

what is the probability of spinning both of the spinners shown below and spinning an even number on both?

Explanation:

Analyze the first spinner

Using the Independent Events knowledge point
The first spinner is divided into 6 equal sectors numbered 1, 2, 3, 4, 5, and 6.
The even numbers on this spinner are 2, 4, and 6.
The probability of spinning an even number on the first spinner is:

$$ P(\text{Even}_1) = \frac{3}{6} = \frac{1}{2} $$

Analyze the second spinner

Using the Independent Events knowledge point
The second spinner is identical to the first, also divided into 6 equal sectors numbered 1, 2, 3, 4, 5, and 6.
The even numbers are 2, 4, and 6.
The probability of spinning an even number on the second spinner is:

$$ P(\text{Even}_2) = \frac{3}{6} = \frac{1}{2} $$

Calculate the compound probability

Using the Compound Probability knowledge point
Since the two spins are independent events, we multiply their individual probabilities:

$$ P(\text{Even on both}) = P(\text{Even}_1) \times P(\text{Even}_2) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $$

Answer:

\(\frac{1}{4}\) (or \(25\%\))