Question

video lesson 5.1 example 4 – finding an experimental probability

1. a spinner has 5 sections, colored red, green, blue, yellow, and purple. each section of the spinner has the same area. the table shows the results of 50 spins. for which color is the experimental probability of stopping on the color the same as the theoretical probability? hint: the theoretical probability of stopping on each color is 1/5.

spinner results
red 5
green 20
blue 3
yellow 10
purple 12

Explanation:

Step1: Recall Experimental Probability Formula

Experimental probability of an event is calculated as $\frac{\text{Number of times the event occurs}}{\text{Total number of trials}}$. Here, total trials (spins) are 50. Theoretical probability for each color is $\frac{1}{5}$ (or 10 out of 50, since $\frac{1}{5} \times 50 = 10$).

Step2: Calculate Experimental Probability for Each Color

• Red: $\frac{5}{50} = \frac{1}{10}$ (not equal to $\frac{1}{5}$)
• Green: $\frac{20}{50} = \frac{2}{5}$ (not equal to $\frac{1}{5}$)
• Blue: $\frac{3}{50}$ (not equal to $\frac{1}{5}$)
• Yellow: $\frac{10}{50} = \frac{1}{5}$ (equal to theoretical probability)
• Purple: $\frac{12}{50} = \frac{6}{25}$ (not equal to $\frac{1}{5}$)

Answer:

yellow