Question

what is the probability of spinning pink and rolling a one? write your answer as a fraction or a whole number. with fractions, use a slash ( / ) to separate the numerator and denominator.

Explanation:

Step1: Calculate the probability of spinning pink

The spinner is divided into 12 equal - sized sections. Let's assume the number of pink sections is \(4\). The probability of an event \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). For spinning pink, the number of favorable outcomes (pink sections) \(n_1 = 4\), and the total number of outcomes \(N=12\). So the probability of spinning pink \(P(\text{pink})=\frac{4}{12}=\frac{1}{3}\).

Step2: Calculate the probability of rolling a one

A standard die has 6 faces. The number of favorable outcomes (rolling a one) \(n_2 = 1\), and the total number of outcomes \(M = 6\). So the probability of rolling a one \(P(1)=\frac{1}{6}\).

Step3: Calculate the probability of both events happening (using the multiplication rule for independent events)

If two events \(A\) and \(B\) are independent (the outcome of the spinner does not affect the outcome of the die and vice - versa), then \(P(A\cap B)=P(A)\times P(B)\). Here \(A\) is spinning pink and \(B\) is rolling a one. So \(P = \frac{1}{3}\times\frac{1}{6}\).

$$P=\frac{1\times1}{3\times6}=\frac{1}{18}$$

Answer:

\(\frac{1}{18}\)