Question

For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.

Let the set B = { −23, −16, −7, −2, 20, 36, 48, 72}. How many ways are there to choose a positive or an odd number from A?

Answer 1

Consider the following set B:

B = {-23, -16, -7, -2, 20, 36, 48, 74}

 

There are four positive numbers in set B (20, 36, 48, 74). So, total number of ways to choose a positive number from set B is 4.

 

There are two odd numbers in set B -23 and -7. So, total number of ways to choose an odd number from set B is equal to 2.

 

As only one number has to be chosen from the set B, either a positive number or an odd number, “Addition Principle” will be used.

 

Addition Principle,

“If one event can occur in m ways and a second event with no common outcomes can occur in n ways, then the first or second event can occur in m + n ways.”

 

Use the addition principle,

The total number of ways to choose a positive or an odd number from B will be equal to the sum of total number of ways to choose a positive number from set B and total number of ways to choose an odd number from set B.

 

So, total number of ways to choose a positive or an odd number from B will be,

4 + 2 = 6

So, total number of ways to choose a positive or an odd number from B will be,

4 + 2 = 6