What is the probability of rolling a 6 with 5 dice?
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Edward D. Collins Show
Let's imagine you are playing a game which uses dice. You are about to roll three of them. You NEED to roll at least one 6. A 6 appearing on any one (or more) of the three dice will win the game for you! What are your chances?
Quite some time ago, I was over at a friend's house watching him and another friend play a board game called Axis & Allies. At one point this exact scenario came up - Kent was planning on rolling three dice and really wanted at least one 6 to appear. He made a comment that with three dice, his chances were 3/6 or 50%. Kent's reasoning was, with one die, the chances of rolling a 6 were 1/6 which is correct. He also believed if he were to roll two dice, his chances were double this or 2/6. This is INCORRECT and this is where his faulty reasoning begins. Knowing a little bit about the laws of probability, I quickly knew the fraction "2/6" for two dice and "3/6" for three dice was incorrect and spent a brief moment computing and then explaining the true percentages. Unfortunately, I do not believe I was successful in explaining to Kent why my figures were correct. Maybe I can do so here. Obviously, with Kent's logic above, if the chances of rolling a 6 with two dice is 2/6 and the chances of rolling a 6 with three dice is 3/6, then the chances of rolling a 6 with six dice would be 6/6 !! 100%?? Of course, this is obviously incorrect. I don't care how many dice you roll, the chances of rolling a 6 will never be 100%. When you roll just one die, there are six different ways the die can land, as shown by the following graphic: Solution: Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows. Probability(Event) = Favourable Outcomes/Total Outcomes = x/n Given, a six-sided die is rolled once. We have to find the probability of rolling either a 5 or a 6. When a six-sided die is rolled, the possible outcomes are : {1, 2, 3, 4, 5, 6} The probability of rolling a 5 is 1/6 The probability of rolling a 6 is 1/6 The probability of rolling either a 5 or a 6 = 1/6 + 1/6 P(5 or 6) = (1 + 1)/6 = 2/6 = 1/3 Therefore, the probability of rolling either a 5 or a 6 is 1/3. Using a six-sided die, what is the probability of rolling either a 5 or a 6?Summary: Using a six-sided die, the probability of rolling either a 5 or a 6 is 1/3. Probability is a numerical description of how likely an event is to occur. The probability of an event is in the range from 0 to 1 where 0 represents the impossibility of the event and 1 represents certainty over the thing. When the probability is higher, then there are more chances to occur the event. Terms used in Probability The terms used in probability are experiment, random experiment, sample space, outcome, and event. Let’s take a look at the definitions of these terms in brief,
What is the probability of getting a sum of 5 or 6 when a pair of dice is rolled?Solution:
Sample ProblemsQuestion 1: Probability of getting at least (minimum) one head while tossing two coins simultaneously. Solution:
Question 2: Probability of getting a sum of even number while rolling two dice. Solution:
Question 3: Probability of getting a sum of multiple of 4 while rolling two dice. Solution:
Question 4: Probability of getting a product of 6 while rolling two dice. Solution:
What is the probability of rolling a 6?There is a 16 chance of rolling a 6 .
What is the probability of rolling a 6 with 6 dice?So similarly, there's a 5/6 chance each die is not 6. The chance they're all not 6 is (5/6)×(5/6)×(5/6)×(5/6)×(5/6)×(5/6)=(5/6)6. So the chance that at least one is a six is 1−(5/6)6. Save this answer.
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