Question

A die is rolled twice. What is the probability that a(n) 3 is rolled on the first roll and an even number on thesecond roll?The probability of rolling a(n) 3 on the first roll and an even number on the second roll is

Answer 1

The events:

• a 3 is rolled on the first roll and

,

• an even number is rolled on the second roll

are independent events. Thus, the probability of both happening is the product of the probabilities of each one happening.

Since the faces of a die are numbered from 1 to 6, one out of 6 is labeled as 3. Thus, the probability that a 3 is rolled is:

`(1)/(6)`

Also, there are 3 even numbers (2,4,6) out of 6 numbers on the faces of the die. Thus, the probability that an even number is rolled is:

`(3)/(6)=(1)/(2)`

Then, multiplying those probabilities, we obtain:

`(1)/(6)\cdot(1)/(2)=(1)/(12)`

Therefore:

The probability of rolling a(n) 3 on the first roll and an even number on the second roll is:

`(1)/(12)`