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

3/64
Start Fraction 3 over 64 End Fraction

1/32
Start Fraction 1 over 32 End Fraction

1/4
Start Fraction 1 over 4 End Fraction

1/16
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 two spins, we first identify the multiples of 4 within the numbers labeled on the circle. The numbers are from 1 to 8, and the multiples of 4 are:

  • 4
  • 8

Therefore, there are 2 multiples of 4 out of a total of 8 sections.

Step 1: Calculate the probability for one spin

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

Step 2: Calculate the probability for two spins

Since the spins are independent events, the probability of landing on a multiple of 4 in both spins is: \[ P(\text{multiple of 4 in both spins}) = P(\text{multiple of 4 in first spin}) \times P(\text{multiple of 4 in second spin}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \]

Conclusion

The probability that the spinner lands on multiple of 4 in both spins is: \[ \boxed{\frac{1}{16}} \]