Question

if you roll a dice twice, what is the possibility of getting a number less than 5 on both rolls?

Answer 1

Solution

Step 1

Write an expression for the probability of an event

$\begin{gathered} \text{If an event is A} \\ P(A)\text{ = }\frac{No\text{ of required events}}{No\text{ of total possible events}} \end{gathered}$

No of the required events can be found with the following table

The numbers(1,2,3,4,5,6) on the vertical are for one dice and the others on the horizontal are for the second dice

No of required of numbers on both dices less than 5 are : 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,3 3,4 4,1 4,2 4,3 4,4. The number of the events are therefore, = 16

No of total events = 36

Step 2

Substitute the values and find the required probability

$\text{Probability of getting numbers less than 5 on both dice = }\frac{16}{36}=\text{ }\frac{4}{9}$