2 dice are rolled1 black and 1 white How many rolls occur in

2 dice are rolled,1 black and 1 white

How many rolls occur in which neither die shows the value 4?

Solution

Given that 2 dice are rolled.

As the number of sides in the dice is not specified, assume the sides of a dice are 6.

And therefore, when 2 dice are rolled, the possible values will go like: {(1, 1), (1, 2), ... (1, 6), ... ... ... (6, 1), ... (6, 6)}.

Which means a total of 36 possible values.

Out of 36 possible rolls, the rolls which will show atleast one 4 on face are: (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (1, 4), (2, 4), (3, 4), (5, 4), (6, 4). That means there are a total of 11 rolls which will have a face of atleast one 4.

And therefore, the number of rolls occur in which neither die shows the value 4 is: 36 - 11 = 25.