Question

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die.

Determine the event that the number falling uppermost on one die is a $4$ and the number falling uppermost on the other die is greater than $4$. (Select all that apply.)

$$\begin{gathered} (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6) \end{gathered}$$

Answer 1

Find the event:

When two dices are rolled sample space is given by

$$\begin{gathered} (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6) \end{gathered}$$

We have to identify all the events where the number on one dice is $4$ and number of other dice is grater then $4$.

The events are

$$\begin{gathered} (4,5)(4,6) \\ \left(5,4\right) \\ \left(6,4\right) \end{gathered}$$

So, there are $4$ possible events.

Hence, the possible events are $(4,5)(4,6)\left(5,4\right)\left(6,4\right)$.