"A fair die" is a dice where all numbers have the same probability of happening when you roll it.
This means, the possible outcomes for the dice are:
S= {1; 2; 3; 4; 5; 6}
And their probabilities are:
P(1)=P(2)=P(3)=P(4)=P(5)=P(6)= 1/6
You roll the dice 4 times and write down the results, the events of interest are:
I'll make it easier:
The event A: "Not having a 2 and not having a 3"
The possible outcomes are
S= {1, 4, 5, 6}
This means that for each roll if you obtain a 1 or a 4 or a 5 or a 6 you fill the criteria of the event. Remember when you say colloquially "it happens A or B" you are refering to a union between two events and can be symbolized: A∪B
So the probability of our event A: "Not having a 2 and not having a 3" can be calculated as:
P(A)= P(1∪4∪5∪6)= P(1)+P(4)+P(5)+P(6)= 1/6+1/6+1/6+1/6= 4/6
The probability of rolling the dice and obtaining no 2 and no 3 is 4/6
