Theoretical Probabilities of Repeated Events Practice

Question

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Question
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An illustration of a circle with four equal differently colored parts labeled 1, 2, 3, 4 clockwise. An arrow starting at the center points toward 1.

The spinner is spun twice. What is the probability of spinning orange (dots) on both spins? Express your answer as a simplified fraction.

(1 point)

Answer 1

To calculate the probability of spinning orange on both spins, first, we need to identify how many sections of the spinner are colored orange.

From your description, it seems like there are four equal sections labeled 1, 2, 3, and 4, and it is not specified which sections are colored. However, let's assume that one section, for example section 1, is the orange section, and the rest (sections 2, 3, and 4) are not orange.

1. The probability of landing on the orange section in one spin is: \[ P(\text{Orange}) = \frac{\text{Number of orange sections}}{\text{Total number of sections}} = \frac{1}{4} \]

2. Since the spins are independent, the probability of landing on orange in both spins is: \[ P(\text{Orange on both spins}) = P(\text{Orange}) \times P(\text{Orange}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \]

Thus, the probability of spinning orange on both spins is \(\frac{1}{16}\).