Chapter 12.8, Problem 17P

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

P(red 6 and blue even)

To determine

Find the probability :

P(red 6 and blue even)

Answer to Problem 17P

  $\frac{1}{12}$

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 6 = 1

Total number of outcomes of blue = 6

Number of favorable outcomes of blue even = 3 = {2,4,6}

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

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

  $\begin{array}{l}P(red\text{ 6 and blue even})=P(red\text{ 6})\cdot P(blue\text{ even)}\\ =\frac{1}{6}\cdot \frac{1}{2}=\frac{1}{12}\end{array}$