Question

A pair of fair dice is rolled together till a sum of either 7 or 11 is obtained. the probability that 7 comes before 11 is?

Answer 1

When rolling a pair of dice, there are 36 possible arrangements.  We can easily ascertain this by the formula of 62.  Six represents the quantity of options each die offers.  Two represents how many dice we have.

 

 

For the probability of seven...

If one die is 6, the other die must be 1.

If one die is 5, the other die must be 2.

If one die is 4, the other die must be 3.

If one die is 3, the other die must be 4.

If one die is 2, the other die must be 5.

If one die is 1, the other die must be 6.

 

There are six possible scenarios.

So 6/62 = 6/36

 

For the probability of 11...

If one die is 6, the other die must be 5.

If one die is 5, the other die must be 6.

 

So 2/62=2/36

 

We must add the two figures...

6/36 + 2/36=8/36=4/18=2/9