Question

a spinner with 10 equally sized slices has 3 blue slices, 2 yellow slices, and 5 red slices. the dial is spun and stops on a slice at random. what is the probability that the dial stops on a blue or yellow slice? write your answer as a fraction in simplest form.

Explanation:

Step1: Calculate the number of favorable outcomes

The number of blue slices is \(3\), and the number of yellow slices is \(2\). So the number of favorable outcomes (blue or yellow) is \(3 + 2=5\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of slices is \(10\). So \(P=\frac{5}{10}\).

Step3: Simplify the fraction

Simplify \(\frac{5}{10}\) by dividing both the numerator and the denominator by their greatest - common divisor, which is \(5\). \(\frac{5\div5}{10\div5}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)