A die is rolled twice.

Question

A die is rolled twice. What is the probability of showing a 3 on the first roll and an even number on the second roll? 

 

 

Answer 1

= (1/6)(1/2) =1/12

Answer 2

When we roll a dice there are 6 possible outcomes S={1, 2, 3, 4, 5, 6}.

The probability of showing a 5 is

P(showing\,a\,5)=\frac{1}{6}

And the probability of showing an even number is

P(even\,number)=\frac{3}{6}

Since rolls are independent from each other so the probability of showing a 5 on the first roll and an even number on the second roll is

P(showing\,a\,5)\cdot P(even\,number)=\frac{1}{6}\cdot \frac{3}{6}=\frac{1}{12}