Chapter 12.8, Problem 15P

You roll a red number cube and a blue number cube. Find each probability

P(red odd and blue less than 4)

To determine

Find the probability :

P(red odd and blue less than 4)

Answer to Problem 15P

  $\frac{1}{4}$

Explanation of Solution

Given:

You roll a red number cube and a blue number cube.

Formula Used:

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

  $P\left(AandB\right)=P\left(A\right)\cdot P\left(B\right)$

Calculation:

A dice has 6 faces with numbers 1 to 6 written on each face.

Total number of outcomes of red = 6

Number of favorable outcomes of red odd = 3 = {1,3,5}

Total number of outcomes of blue = 6

Number of favorable outcomes of blue less than 4 = 3 = {1,2,3}

  $P(red\text{ odd})=\frac{\text{favourable outcomes }}{total\text{ number of outcomes}}=\frac{3}{6}=\frac{1}{2}$

  $P(blue\text{ less than 4})=\frac{\text{favourable outcomes }}{total\text{ number of outcomes}}=\frac{3}{6}=\frac{1}{2}$

  $\begin{array}{l}P(red\text{ odd and blue less than 4})=P(red\text{ odd})\cdot P(blue\text{ less than 4)}\\ =\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}\end{array}$