Bivariate Data Analysis & Probability Unit Test

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Question
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

132
Start Fraction 1 over 32 End Fraction

364
Start Fraction 3 over 64 End Fraction

14
Start Fraction 1 over 4 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 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.