Question Continuation
Rolling a 3 is an outcome of which of the following events? Select all correct answers.
Select all that apply:
1. E OR L
2. E′ AND L
3. E AND L
4. E′ OR L′
5. L′
6. E AND L′
Answer:
1. E OR L
2. E' AND L
4. E' OR L'
Step-by-step explanation:
Given
S = Sample Space = {1,2,3,4,5,6}
E = the event of showing an even number on top = {2,4,6}
L the event of showing a number less than 4 = {1,2,3}
Test Item = {3}
From the above, we can easily get E' and L'
E' means items not in E but in Sample Space; in other words, Odd numbers
E' = {1,3,5}
L' means items not in L but in Sample Space; in other words, numbers greater than or equal to 4
L = {4,5,6}
OR Rule
For a statement to be true, then at least one of the conditions must be true.
AND Rule
For a statement to be true, all conditions must be true.
So,
1. E OR L
E = {2,4,6}
L = {1,2,3}
E OR L = {1,2,3,4,6}
This is true for a roll that gives an outcome of 3
2. E' AND L
E' = {1,3,5}
L = {1,2,3}
E AND L = {1,3}
This is true for a roll that gives an outcome of 3
3. E AND L
E = {2,4,6}
L = {1,2,3}
E AND L = {2}
This is not true for a roll that gives an outcome of 3
4. E′ OR L′
E' = {1,3,5}
L' = {4,5,6}
E' OR L' = {1,3,4,5,6}
This is true for a roll that gives an outcome of 3
5. L′
L' = {4,5,6}
This is not true for a roll that gives an outcome of 3
6. E AND L′
E = {2,4,6}
L' = {4,5,6}
E AND L' = {4,6}
This is not true for a roll that gives an outcome of 3
