a Use geometric probability. What is the area of the section of the spinner corresponding to the number 3 in terms of the area of the spinner?
B
b Use geometric probability. What is the combined area of the sections of the spinner corresponding to odd numbers in terms of the area of the spinner?
A
a 1/8
B
b 1/2
Practice makes perfect
a A spinner is divided into 8 equal sections. We want to find the probability that if the arrow lands on a number, it will land on 3. We will use geometric probability. The probability of the arrow landing on 3 is the ratio of the area of the section corresponding to 3 to the area of the spinner.
Let's call the area of the spinner A. Since the spinner is divided into 8 equal sections, the area of each section, including the section corresponding to the number 3, is 18A. Therefore, the probability that the arrow lands on 3 is the ratio of 18A to A.
b We want to find the probability that if the arrow lands on a number, it lands on an odd number. We will use geometric probability. The probability of the arrow landing on an odd number is the ratio of the area of sections corresponding to odd numbers to the area of the spinner.
As we can see, there are 4 odd numbers on the spinner. We already know from Part A that if we call the area of the spinner A, each section has area 18A. This means that the combined area of all the sections corresponding to odd numbers is 48A. Therefore, our probability is the ratio of 48A to A.
