Throwing Dice Probability

Probability is the likelihood of the occurrence of an event. Probabilities are always numbers between 0 (impossible) and 1(possible), inclusive. Set of possible outcomes of a particular experiment is called as event. The set of all possible outcomes of an experiment is referred to as sample space. For example, when throwing a dice, the sample space {1, 2, 3, 4, 5, 6}.

Throwing Dice Probability – Example Problems

Example 1: When throwing a single dice what is the probability of getting less than 4?

Solution:

Sample space S = {1, 2, 3, 4, 5, 6}, n(S) = 6

Let A be the event of getting less than 4, (1, 2, 3), n(A) = 3

P(A) = `(n(A))/(n(S)) ` = `3/6` = `1/2`

Example 2: When throwing two dice, what is the probability of getting a sum is less than 7 or 8?

Solution:

Sample space n(S) = 6 * 6 = 36.

Let A be the event of getting a sum is less than 7.

= {{1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1)

(3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}

n(A) = 15

P(A) = `(n(A))/(n(S))` = `15/36` = `5/12`

Let B be the event of getting a sum is less than 8

= {{1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1)

(3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1)}

n(B) = 21

P(B) = `(n(B))/(n(S))` = `21/36` = `7/12`

P(A or B) = P(A) + P(B) = `5/12` + `7/12` = `12/12` = 1

P(A or B) = 1

Example 3: When throwing two dice, what is the probability of getting a sum is greater than 7 and 8?

Solution:

Sample space n(S) = 6 * 6 = 36.

Let A be the event of getting a sum is greater than 7.

= {{2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(A) = 15

P(A) = `(n(A))/(n(S))` = `15/36` = `5/12`

Let B be the event of getting a sum is greater than 8

= {{3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

n(B) = 10

P(B) = `(n(B))/(n(S))` = `21/36` = `10/36` = `5/18`

P(A and B) = P(A) · P(B) = `5/12` · `5/18` = `25/216`

P(A or B) = `25/216`

I am planning to write more post on Tree Diagrams Probability and its example and, Probability Equations and its problem with solution. Keep checking my blog.

Throwing Dice Probability – Practice Problems

Problem 1: When throwing two dice, what is the probability of getting a sum exactly 10?

Problem 2: When throwing two dice, what is the probability of getting a sum exactly 5?

Answer: 1) `1/12` 2) `1/9`