Chapter 12.8, Problem 14P

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

P(red greater than 2 and blue 4)

To determine

Find the probability :

P(red greater than 2 and blue 4)

Answer to Problem 14P

  $\frac{1}{9}$

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 greater than 2 = 4 = {3,4,5,6}

Total number of outcomes of blue = 6

Number of favorable outcomes of blue 4 = 1

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

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

  $\begin{array}{l}P(red\text{ greater than 2 and blue 4})=P(red\text{ greater than 2})\cdot P(blue\text{ 4)}\\ =\frac{2}{3}\cdot \frac{1}{6}=\frac{1}{9}\end{array}$