To determine the probability that the spinner lands on both multiples of 4 in both spins, we first need to identify the multiples of 4 within the range of numbers on the spinner (1 to 8).
The multiples of 4 in this range are:
- 4 (since \(4 \times 1 = 4\))
- 8 (since \(4 \times 2 = 8\))
So, the multiples of 4 are 4 and 8.
There are 2 favorable outcomes (4 and 8) out of a total of 8 possible outcomes (1 through 8) when the spinner is spun once.
The probability of landing on either multiple of 4 in one spin is:
\[ P(\text{multiples of 4}) = \frac{\text{number of favorable outcomes}}{\text{total outcomes}} = \frac{2}{8} = \frac{1}{4} \]
Now, since the spinner is spun twice, we multiply the probabilities of these independent events:
\[ P(\text{multiples of 4 in both spins}) = P(\text{multiples of 4}) \times P(\text{multiples of 4}) \]
\[ P(\text{multiples of 4 in both spins}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \]
Thus, the probability that the spinner lands on both multiples of 4 in both spins is:
\[ \frac{1}{16} \]
The correct response is:
Start Fraction 1 over 16 End Fraction.