Probability - Throwing One Dice

A number of questions can be framed on this:

• Probability of getting an even/odd number
• Probability of getting a number greater/lesser than 3
• Probability of getting an even number greater than 3

Solved Examples

What is the probability of getting an even number on throwing a dice once?

There are six numbers on a dice: 1, 2, 3, 4, 5, and 6. Hence total number of outcomes possible on throw of a dice once are six (any one of the six numbers can show up). There are three even numbers on a dice: 2, 4 and 6. Hence total number of outcomes favorable to us are three (since any one of these three even numbers can show up). Hence by applying the formula for theoretical probability, we get,

`P("outcome") = "number of favorable outcomes"/"total number of possible outcomes"`

`P("even number") = 3/6 = 1/2`

Hence the probability of getting an even number when throwing a dice once is 1/2. Similarly, the probability of getting an odd number on a single throw of a dice is 1/2.

What is the probability of getting a number greater than  4 on a single throw of a dice?

There are six numbers on a dice: 1, 2, 3, 4, 5, and 6. Hence total number of outcomes possible on throw of a dice once are six (any one of the six numbers can show up). There are two numbers greater than four on a dice: 5 and 6. Hence total number of outcomes favorable to the outcome are two. Hence by applying the formula for theoretical probability, we get,

`P("outcome") = "number of favorable outcomes"/"total number of possible outcomes"`

`P("number greater than 4") = 2/6 = 1/3`

Hence the probability of getting a number greater than 4 when throwing a dice once is 1/3. Similarly other questions can be framed on it. You can solve the exercise for more practice. The above two questions can be combined to form another question:

What is the probability of getting an even number greater than 3 on a single throw of a dice?

Again we will use the same procedure in solving the problem. There are six numbers on a dice: 1, 2, 3, 4, 5, and 6. Hence total number of outcomes possible on throw of a dice once are six (any one of the six numbers can show up). There are three numbers greater than three on a dice: 4, 5 and 6. Out of these three number, there are two even numbers: 4 and 6. Hence total number of outcomes favorable to the outcome are two.
Hence by applying the formula for theoretical probability, we get,

`P("outcome") = "number of favorable outcomes"/"total number of possible outcomes"`

`P("even number greater than 3") = 2/6 = 1/3`

Hence the probability of getting an even number greater than 3 when throwing a dice once is 1/3.

Worksheet

Q.No.	Question	Answer
1	What is the probability of getting the number 6 on a single throw of a dice?	1/6
2	What is the probability of getting the number 7 on a single throw of a dice?	1/7
3	What is the probability of getting an odd number on a single throw of a dice?	1/2
4	What is the probability of getting a number greater than 2 on a single throw of a dice?	2/3
5	What is the probability of getting a number lesser than or equal to three on a single throw of a dice?	2/3
6	What is the probability of getting an odd number lesser than 5 on a single throw of a dice?	1/3
7	What is the probability of getting an even number greater than or equal to 5 on a single throw of a dice?	0