Question

Dice. Refer to the image below and for each of the following events, list the outcomes that constitute the event in words

1. (not A)
2. (A & B )
3. (B or C)

When one die is rolled, following outcomes are possible :

Short answer

1. Here the potential outcomes are 1, 3 and 5

   In words, the die shows odd

2. Here the potential outcomes are 4 and 6

   In words, the die shows 4 or 6

3. Here the potential outcomes are 1, 2, 4, 5 and 6

In words, the die not shows 3

Step-by-step solution

Part (a)   Step 1.  Given information

The potential outcomes when the dice rolled are 1,2,3,4,5,6.

A= the die shows even.

B= the die shows 4 or more.

C= the die shows at most 2

D= the die shows 3.

Part (a)   Step 2.   Utilized principle and Equation

The probability of an event lie between 0 to 1 and both are applicable.

$Probabilityofaneventis:P\left(E\right)=\frac{No.ofdesiredoutcomes}{Totalno.ofoutcomes}$

Part  (a)   Step 3. Calculation

It is provided that

A= when the die shows even.

Potential outcomes are 2,4 and 6

B= when the die shows 4 or more.

Potential outcomes are 4,5 and 6

C= when the die shows at most 2

Potential outcomes are 1 and 2

D= when die shows 3.

Potential outcome is 3

Part (a)  Step 4. Conclusion

Here the potential outcomes are 1, 3 and 5

In words, the die shows odd

Part  (b)  Step 1. Calculation 

It is provided that

A= when the die shows even.

Potential outcomes are 2,4 and 6

B= when the die shows 4 or more.

Potential outcomes are 4,5 and 6

C= when the die shows at most 2

Potential outcomes are 1 and 2

D= when die shows 3.

Potential outcome is 3

Part (b)  Step 2. Conclusion

Here the potential outcomes are 4 and 6

In words, the die shows 4 or 6

Part (c)  Step 1. Calculation 

It is provided that

A= when the die shows even.

Potential outcomes are 2,4 and 6

B= when the die shows 4 or more.

Potential outcomes are 4,5 and 6

C= when the die shows at most 2

Potential outcomes are 1 and 2

D= when die shows 3.

Potential outcome is 3

Part (c)  Step 2. Conclusion

Here the potential outcomes are 1, 2, 4, 5 and 6

In words, the die does not shows 3