**Question:**

**A dice is rolled once. What is the probability that the number on top will be**

**(a) Odd**

**(b) Greater than 5**

**(c) A multiple of 3**

**(d) Less than 1**

**(e) A factor of 36**

**(f) A factor of 6**

**Solution:**

A dice is rolled once, the possible outcomes are 1, 2, 3, 4, 5 and 6.

Then,

The probability that the number on top will be

(a) Odd

Odd numbers in the dice are 1, 3, 5

Then,

Probability = total number of odd numbers/ Total number of outcomes

= 3/6 … [divide numerator and denominator by 3]

= ½

(b) Greater than 5

Greater than 5 is 6

Then,

Probability = total number Greater than 5/ Total number of outcomes

= 1/6

(c) A multiple of 3

Multiple of 3 = 3 and 6

Then,

Probability = total number of multiple of 3/ Total number of outcomes

= 2/6 … [divide numerator and denominator by 2]

= 1/3

(d) Less than 1

There is no number is less than 1.

So, probability of less than 1 = 0

(e) A factor of 36

Factors of 36 are 1, 2, 3, 4 and 6

Probability = total number of factor of 36/ Total number of outcomes

= 5/6

(f) A factor of 6

Factors of 6 are 1, 2, 3 and 6

Probability = total number of factor of 6/ Total number of outcomes

= 4/6 … [divide numerator and denominator by 2]

= 2/3