You roll a six-sided die. Find the probability of each of the following scenarios.

(a) Rolling a 4 or a number greater than 3

(b) Rolling a number less than 5 or an even number

(c) Rolling a 4 or an odd number

Step-by-step explanation:

A six-sided die has the following outcomes in the six sides, 1,2,3,4,5,6

a) To determine the probability of rolling a 4 or a number greater than 3 ,

There are a total of six possible outcomes when a die is rolled

You can get a 4 once in a throw.

Probability of rolling a 4 is 1/6

Also, there are three numbers greater than 3.

Probability of rolling a number greater than 3 is 3/6 = 1/2

The events are non mutually exclusive because the possibility of a 4 is common to both outcomes. We would subtract the probability of one 4 which equals 1/6. Therefore

The probability of rolling a 4 or a number greater than 3 is 1/6 + 1/2 - 1/6 = 1/2

(b) Rolling a number less than 5 or an even number

There are 4 numbers that are lesser than 5.

Probability of rolling a number less than 5 is 4/6 = 2/3

There are 3 even numbers

Probability of rolling an even number is 3/6 = 1/2

The events are non mutually exclusive because the possibility of a 2 and a 4 is common to both outcomes. We will subtract the probability of a 2 and a 4 which equals 2/6 = 1/3. Therefore

The probability of rolling a number less than 5 or an even number is

2/3 + 1/2 - 1/3 = 5/6

(c) Rolling a 4 or an odd number

You can get a 4 once in a throw.

Probability of rolling a 4 is 1/6

There are three odd numbers. Therefore,

Probability of rolling an odd number is 3/6 = 1/2

Therefore

Rolling a 4 or an odd number is

1/2 + 1/6 = 4/6 = 2/3