Question

You roll a 6-sided die two times.What is the probability of rolling a number less than 6 and then rolling a 4?Simplify your answer and write it as a fraction or whole number.

Answer 1

We can find the probability of an event A to occur using the formula:

`P(A)=\frac{favorable\text{ }outcome}{total\text{ }outcome}`

In a dice there are 6 faces, thus the total outcome is 6.

First, we need to find the probability of getting a number less than 6. The outcomes that satisfy the condition are 1, 2, 3, 4 and 5. Thus, the favorable outcome is 5.

Then:

`P(rolling\text{ }less\text{ }than\text{ }6)=(5)/(6)`

On the second roll, we want to get a 4. This is the only favorable outcome. Thus:

`P(rolling\text{ }4)=(1)/(6)`

These two events are independent because the outcome in the first roll does not affect the outcome in the second roll. To find the probability of two independent events (A and B) occurring, we use:

`P(A\text{ }and\text{ }B)=P(A)\cdot P(B)`

Then:

`P(rolling\text{ }less\text{ }than\text{ }6\text{ }and\text{ }rolling\text{ }4)=P(rolling\text{ }less\text{ }than\text{ }6)\cdot P(rolling\text{ }4)`
`P(rolling\text{ }less\text{ }than\text{ }6\text{ }and\text{ }rolling\text{ }4)=(5)/(6)\cdot(1)/(6)=(5)/(36)`

The answer is 5/36