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′

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

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !