Use the image to answer the question.

An illustration of a circle with eight equal parts labeled from 1 through 8 clockwise. An arrow starting in part 1 passes through the center to point into part 5.

The spinner is spun twice. What is the probability that the spinner lands on both multiples of 4 in both spins?

(1 point)
Responses

14
Start Fraction 1 over 4 End Fraction

364
Start Fraction 3 over 64 End Fraction

132
Start Fraction 1 over 32 End Fraction

116
Start Fraction 1 over 16 End Fraction
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1 answer

To determine the probability that the spinner lands on both multiples of 4 in both spins, we first identify the multiples of 4 within the circle sections numbered from 1 to 8.

The multiples of 4 in this range are:

  • 4
  • 8

So, there are 2 favorable outcomes (4 and 8) out of a total of 8 possible outcomes on the spinner.

The probability of landing on a multiple of 4 in one spin is: \[ P(\text{multiple of 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{8} = \frac{1}{4} \]

Since the spins are independent, to find the probability of landing on a multiple of 4 on both spins, we multiply the probabilities of each spin: \[ P(\text{both spins are multiples of 4}) = P(\text{multiple of 4}) \times P(\text{multiple of 4}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \]

Thus, the probability that the spinner lands on both multiples of 4 in both spins is: \[ \frac{1}{16} \]

Therefore, the answer is: \[ \frac{1}{16} \]