Dive into a practical and easy-to-follow explanation of a spinner probability problem perfect for Key Stage 3 students. Discover how to calculate expected outcomes based on angles and spins.

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The Question:

Carol has a fair spinner. It has a purple section, a blue section and a green section. Each section is a different size. She spins it 240 times.

a) The central angle of the purple section is 15 degrees. How many times would you expect the spinner to land on purple?

b) Carol expects the spinner to land on blue 180 times. What is the central angle of the blue section? Give your answer in degrees.

Check out the full breakdown below to see how to solve this step by step!

Part (a): How many times would the spinner land on purple?

1. Understand the problem:
   The spinner is divided into sections. Each section has a central angle. This is the angle at the center of the circle. The purple section has a central angle of 15 degrees. Since a full circle is 360 degrees, the purple section is part of this total.
2. Find the fraction of the spinner that is purple:
   Identify the part of the spinner that is purple. To do this, you need to divide the angle of the purple section by the total angle of a circle. Fraction of purple = 15/360. Simplify the fraction: 15/360=1/24.
3. Calculate how many times it lands on purple:
   If the spinner is spun 240 times, determine the fraction of purple.
   Then, multiply this fraction by the total number of spins.
   To find the expected number of purple spins, calculate using the formula: 1/24 × 240 = 10.
   Answer: The spinner would land on purple 10 times.

Part (b): What is the central angle of the blue section?

1. Understand the problem:
   Carol expects the spinner to land on blue 180 times out of 240 spins.
   First, we need to determine the fraction of spins that are blue.
   Then, we can find the central angle of the blue section.
   
2. Find the fraction of blue:
   The fraction of spins that land on blue is: Fraction of blue= 180/240
   ​Simplify the fraction: 180/240=3/4
3. Find the central angle for blue:
   The blue section takes up 3/4 of the spinner. The angle for blue is calculated as follows: Blue angle = (3/4) × 360.
   Multiply, and you get: Blue angle = 270 degrees.
   Answer: The central angle of the blue section is 270 degrees.

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Final Answers:

• (a) The spinner lands on purple 10 times.
• (b) The central angle of the blue section is 270 degrees.