Question

a spinner with 10 equally sized slices has 2 blue slices, 4 yellow slices, and 4 red slices. the dial is spun and stops on a slice at random. what is the probability that the dial stops on a blue slice? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine the formula for probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

Step2: Identify the number of favorable and total outcomes

The number of blue slices (favorable outcomes) is \(2\). The total number of slices is \(10\).

Step3: Calculate the probability

Substitute into the formula: \(P = \frac{2}{10}\).

Step4: Simplify the fraction

Divide numerator and denominator by their greatest - common divisor (GCD). The GCD of \(2\) and \(10\) is \(2\). So, \(\frac{2\div2}{10\div2}=\frac{1}{5}\).

Answer:

\(\frac{1}{5}\)