Question

A single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 2 the second time.Find the probability of rolling an odd number the first time and a number greater than 2 the second time.

Answer 1

Step 1 :

We need to understand that the single die was rolled twice.

We need to get the probability of rolling the odd number and

a number greater than 2, the second time.

Step 2 :

We need to calculate the probability of rolling an odd number the first time:

( 1, 3, 5 )

Probability ( rolling an odd number the first time ) =

`(3)/(6)`

Step 3 :

We need to calculate the probability of getting a number greater than 2 the second time; ( 3, 4, 5,6 )

Probability ( getting a number greater than 2 the second time ) =

`(4)/(6)`

Step 4 :

Then, we need to find the probability of rolling an odd number the first time and a number greater than 2 the second time =

`\begin{gathered} \text{Probability ( rolling an odd number the first time ) X } \\ \\ \text{Probability ( }a\text{ number greater than 2 the second time )} \end{gathered}`

=

`\begin{gathered} (3)/(6)\text{ x }(4)/(6)\text{ } \\ =(12)/(36) \\ =(1)/(3) \end{gathered}`

CONCLUSION:

The probability of rolling an odd number the first time and a number greater than 2 the second time =

`(1)/(3)`