Dice Roll Probability

Many games use dice to decide the moves of players across the games. A dice has six possible outcomes and the outcomes of a dice is a game of chance and can be obtained by using the concepts of probability. Some games also use two dice, and there are numerous probabilities that can be calculated for outcomes using two dice. Let us now check the outcomes, their probabilities for one dice and two dice respectively.

Rolling One Dice

The total number of outcomes on rolling a die is 6, and the sample space is {1, 2, 3, 4, 5, 6}. Here we shall compute the following few probabilities to help in better understanding the concept of probability on rolling one dice.

• P(Even Number) = Number of even number outcomes/Total Outcomes = 3/6 = 1/2
• P(Odd Number) = Number of odd number outcomes/Total Outcomes = 3/6 = 1/2
• P(Prime Number) = Number of prime number outcomes/Total Outcomes = 3/6 = 1/2

Rolling Two Dice

The total number of outcomes on rolling two dice is 6² = 36. The following image shows the sample space of 36 outcomes on rolling two dice.

Let us check a few probabilities of the outcomes from two dice. The probabilities are as follows.

• Probability of getting a doublet(Same number) = 6/36 = 1/6
• Probability of getting a number 3 on at least one dice = 11/36
• Probability of getting a sum of 7 = 6/36 = 1/6

As we see, when we roll a single die, there are 6 possibilities. When we roll two dice, there are 36 possibilities. When we roll 3 dice we get 216 possibilities. So a general formula to represent the number of outcomes on rolling ‘n’ dice is 6ⁿ.

Probability of Drawing Cards

A deck containing 52 cards is grouped into four suits of clubs, diamonds, hearts, and spades. Each of the clubs, diamonds, hearts, and spades have 13 cards each, which sum up to 52. Now let us discuss the probability of drawing cards from a pack. The symbols on the cards are shown below. Spades and clubs are black cards. Hearts and diamonds are red cards.

The 13 cards in each suit are ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king. In these, the jack, the queen, and the king are called face cards. We can understand the card probability from the following examples.

• The probability of drawing a black card is P(Black card) = 26/52 = 1/2
• The probability of drawing a hearts card is P(Hearts) = 13/52 = 1/4
• The probability of drawing a face card is P(Face card) = 12/52 = 3/13
• The probability of drawing a card numbered 4 is P(4) = 4/52 = 1/13
• The probability of drawing a red card numbered 4 is P(4 Red) = 2/52 = 1/26