Demonstration of Working with AND and OR
 Topic Index | Algebra Index | Regents Exam Prep Center

Two die are thrown. 

 What is the probability of throwing a 4 on the first die
and a 3 on the second die?

What is the probability of throwing a 4 on the first die
or a 3 on the second die?

Supplies: 

graph paper or grid chalkboard, grids, colored chalk or markers.

Grids: 

prepare two grids as shown below using graph paper or grid board.  Each dot on the grid represents one possible outcome of throwing the dice.

 

Demonstration for AND

What is the probability of throwing a 4 on the first die and a 3 on the second die?

There is only ONE location on the grid which represents a throw of 4 on the first die and a 3 on the second die.

This shows that the probability is 1/36.

 

 

Demonstration for OR

What is the probability of throwing a 4 on the first die or a 3 on the second die?

The red circles represent the number of ways a 4 can appear on the first die.  The green squares represent the number of ways a 3 can appear on the second die.

The grid clearly shows that one location (4,3) is marked twice.  Because of this overlap, there are actually only 11 out of 36 ways to throw 4 on the first die or 3 on the second die.  The probability is 11/36.