Question

You roll a 6-sided die two times.What is the probability of rolling a 6 and then rolling a number less than 2?Simplify your answer and write it as a fraction or whole numb

Answer 1

We are asked to determine the probability of rolling a 6 and then rolling a number less than 2. To do that we will use the product rule probabilities since we want to find the probability of two independent events happening:

`P(AandB)=P(A)P(B)`

Where:

`\begin{gathered} A=\text{ rolling a 6} \\ B=\text{ rolling a number less than 2} \end{gathered}`

To determine the probability of rolling a 6 we need to have into account that there are 6 possible outcomes out of which only one is a 6. Therefore, the probability is:

`P(A)=(1)/(6)`

To determine the probability of B we need to have into account that in a 6-sided die the numbers that are less than 2 are (1), this means that there is only one number less than 2 out of 6 possible numbers. Therefore, the probability is:

`P(B)=(1)/(6)`

Now, we substitute in the product rule:

`P(AandB)=((1)/(6))((1)/(6))`

Solving the product:

`P(AandB)=(1)/(36)`

Therefore, the probability is 1/36.