Chapter 12.8, Problem 18PPE

To determine

To find: The probability that number obtained is blue and green both less than 6.

Answer to Problem 18PPE

The required probability is $\frac{25}{36}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Each cube has 5 outcomes that are less than 6.

Find the probability that the number is less than 6.

  $\begin{array}{c}P\left(\text{blue}\text{less}\text{than}\text{6}\right)=\frac{5}{6}\\ P\left(\text{green}\text{less}\text{than}\text{6}\right)=\frac{5}{6}\end{array}$

The blue cube's roll and the green cube's are independent, so simply multiply the corresponding probabilities together to get the probability that both occur.

Find the required probability as follows.

  $\begin{array}{c}P\left(\text{blue}\text{and}\text{green}\text{both}\text{less}\text{than}\text{6}\right)=\frac{5}{6}\times \frac{5}{6}\\ =\frac{25}{36}\end{array}$

Therefore, the required probability is $\frac{25}{36}$ .