b Use the the probability of the complement of the given event.
A
a 1112, or about 92 %
B
b 1318, or about 72 %.
Practice makes perfect
a We have two six-sided dices, and there are 36 possible outcomes when they are rolled. We want to find the probability that the sum is not 4. To do so we will find the the probability of the complement of the given event that is the sum is 4. Then we will subtract it from the sum of the probabilities of all outcomes in a sample space — 1.
P(sum is not4)=1-P(sum is4)
Now we will list the outcomes when the sum of the numbers on two dices is 4.
Number on the First Dice
Number on the Second Dice
Sum
1
3
4
2
2
4
1
3
4
The number of favorable outcomes is 3. Also, we know that total number of outcomes is 36. We will find the theoretical probability if the sum is 4.
P(sum is4)&=3/36
&= 1/12
We found the probability of the complement of the event. We will use it to find the desired probability.
We obtained the probability of the sum of the numbers on two dices is not four as 1112, or about 92 %.
b In this exercise we will find the probability of the event that the sum of the numbers on the dices is greater than 5. Since the number of favorable outcomes of the complement event that is the sum is less than or equal to 5 will be less, we will use the complement of the event to find the probability of the given event. We will first list the possible favorable outcomes.
Number on the First Dice
Number on the Second Dice
Sum
1
1
2
1
2
3
1
3
4
1
4
5
2
1
3
2
2
4
2
3
5
3
1
4
3
2
5
4
1
5
The number of the favorable outcomes for the complement of the event is 10. We also know the total number of outcomes, 36. We will find the theoretical probability of the complement.
P(sum is less than or equal to5)&=10/36
&= 5/18
Since we found the probability of the complement, we can find the desired probability.
P(sum is greater than5)=1-P(sum is less than or equal to5)
