Question

A red die and a blue die are thrown at the same time. List all the possible outcomes in a systematic way. Find the probability of obtaining a total of $10$.

Answer 1

Step 1: Finding all the possible outcomes

When two die are thrown at the same time the total possible outcomes are:

The total number of outcomes is $36$.

Step 2: Finding the probability of getting a total of $10$

The die combinations which gives total of $10$ are:

$\left(4,6\right),\left(5,5\right),\left(6,4\right)$

So the number of favorable outcomes are $3$.

The formula for the probability is expressed as,

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Substitute the number of favorable outcomes as $3$ and the total number of outcomes as $36$.

$$\begin{gathered} \Rightarrow P\left(atotalof10\right)=\frac{3}{36} \\ \therefore P\left(atotalof10\right)=\frac{1}{12} \end{gathered}$$

Hence, the probability of getting a total of $10$, by rolling two die is $\frac{1}{12}$.