Chapter 12.8, Problem 7P

You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find each probability.

P(even or less than 8)

To determine

Find the probability :

P(even or less than 8)

Answer to Problem 7P

  $\frac{5}{6}$

Explanation of Solution

Given:

You spin a spinner that has 12 equal-sized sections numbered 1 to 12.

Formula Used:

  $P(E)=\frac{\text{Favourable outcomes of E}}{\text{total number of outcomes}}$

P(A or B) = P(A) + P(B) − P(A and B)

Calculation:

Total number of sections = 12

Number of favorable outcomes that are even numbers = 6 ={2,4,6,8,10,12}

Number of favorable outcomes that are less than 8 = 7 = {1,2,3,4,5,6,7}

Number of favorable outcomes that are even and less than 8 = 3 = {2,4,6}

  $P(even)=\frac{\text{favourable outcomes }}{total\text{ number of outcomes}}=\frac{6}{12}=\frac{1}{2}$

  $P(\text{less than 8})=\frac{\text{favourable outcomes }}{total\text{ number of outcomes}}=\frac{7}{12}$

  $P(even\text{ and less than 8})=\frac{\text{favourable outcomes }}{total\text{ number of outcomes}}=\frac{3}{12}=\frac{1}{4}$

  $\begin{array}{l}P(evenor\text{ less than 8})=P(even)+P(less\text{ than 8})-P(even\text{ and less than 8})\\ =\frac{1}{2}+\frac{7}{12}-\frac{1}{4}=\frac{6+7-3}{12}=\frac{10}{12}=\frac{5}{6}\end{array}$