A standard six-sided die shows a number, 1, 2, 3, 4, 5, or 6, on each of its sides. You roll the die once. Let E be the event of rolling the die and it showing an even number on top and L be the event of rolling a number less than 4. Rolling a 3 is an outcome of which of the following events? Select all correct answers.

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