We are considering that we have 2 dices with 6 faces each (so, the probability to gettig any face in any dish is 1/6). To get an 11, we only have two ways to obtain it:
Dice 1= 6 and Dice 2 =5
or
Dice 1= 5 and Dice 2 =6
So, the probability of the event is given as:
P(Dice1=5 ∧ Dice2=6) ∪ P(Dice1=6 ∧ Dice2=5) = P(Dice1=5) x P(Dice2=6) + P(Dice1=6) x P(Dice2=5) = 1/6 x 1/6 + 1/6 x 1/6 = 1/36 + 1/36 = 2/36 = 1/18.
As 1/18 = 0,055, and 0,055 > 0,05, we consider the event as not significative (according to the definition of significance in the sentence).
When you throw a dice, the total number of options that you can get is the product of the number of options for each dice, this means that the total number of combinations is:
c = 6*6 = 36 combinations.
Now, the combinations where the dice add to 11 are:
5 in one dice and 6 in the other.
6 in one dice and 5 in the other.
so out of 36 combinations, we have 2 options where we have an 11.
then the probability is the combinations that add to 11 divided by the total number of combinations:
p = 2/36 = 1/18 = 0.056
the probability is greater than 0.05, so it is significant.
