Assuming we have a standard six-sided die, the odds of rolling a particular value are 1/6. There is an equal probability of rolling each of the numbers 1-6. But, when we have two dice, the odds are not as simple. For example, there's only one way to roll a two (snake eyes), but there's a lot of ways to roll a seven (1+6, 2+5, 3+4). Let's count how many ways there are to get each value, 2 through 12:
If we want to calculate the probability of rolling, say, a five, we need to divide the number of ways to get 5 by the total possible combinations of two dice. How many total combinations are possible from rolling two dice? Since each die has 6 values, there are \(6*6=36\) total combinations we could get. If you add up the numbers in the total column above, you'll get 36. So, we can calculate the probabilities of each outcome:
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Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty. The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).
What is Sample Space? All the possible outcomes of an event are called Sample spaces. Examples-
Types of EventsIndependent Events: If two events (A and B) are independent then their probability will be
Example: If two coins are flipped, then the chance of both being tails is 1/2 * 1/2 = 1/4 Mutually exclusive events:
Example: The chance of rolling a 2 or 3 on a six-faced die is P (2 or 3) = P (2) + P (3) = 1/6 + 1/6 = 1/3 Not Mutually exclusive events: If the events are not mutually exclusive then
What is Conditional Probability? For the probability of some event A, the occurrence of some other event B is given. It is written as P (A ∣ B)
Example- In a bag of 3 black balls and 2 yellow balls (5 balls in total), the probability of taking a black ball is 3/5, and to take a second ball, the probability of it being either a black ball or a yellow ball depends on the previously taken out ball. Since, if a black ball was taken, then the probability of picking a black ball again would be 1/4, since only 2 black and 2 yellow balls would have been remaining, if a yellow ball was taken previously, the probability of taking a black ball will be 3/4. What’s the probability of rolling a sum of 6 on two dice?Solution:
Similar QuestionsQuestion 1: What is the probability of getting 6 on both dice? Solution:
Question 2: What is the probability of getting pair with 6 on only one dice? Solution:
Question 3: What is the probability of getting a pair with at-least one 6 on two dices? Solution:
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