Q. 1.2 - A First Course in Probability

Question

How many outcome sequences are possible when a die is rolled four times, where we say, for instance, that the outcome is 3, 4, 3, 1 if the first roll landed on 3, the second on 4, the third on 3, and the fourth on 1? 

Step-by-Step Solution

Answer

The number of  possible sequences  are $6\times 6\times 6\times 6=6^4$ 

Step 1 .Given information

Here a die is rolled four times, we have to find out the possible number of  sequences of out comes

Step 2 . Finding the number of possible sequences of outcomes

 If a die is rolled for on time,   the outcomes are $\left\{1,2,3,4,5,6\right\}$ , that is 6 outcomes. Then the die is rolled four  times, the outcomes are repeated four  times  $that is 6\times 6\times 6\times 6=6^4 times$