When you roll two dice, you have a 30.5 % chance at least one 6 will appear. This figure can also be figured out mathematically, without the use of the graphic.
What is the probability of getting at least 6 for one time when the dice is rolled for 6 times?
Here, number of times that we get six (X) follows binomial distribution with n=6 and p= 1/6. Thus, the probability of getting at least one six is 0.6652.
What is the cardinality of the event such that 6 appears at least 1 time if you roll two dice?
Each die has 6 possible outcomes. 1 through 6. Now, if BOTH dice must show a 6 the solution is simple: 1/6 * 1/6 = 1/36.
What is the probability of getting three dots?
Probability of 3 dots lying on the same edge = 4*(1/4)^3 = 1/16 Probability of 2 dots lying on same edge with another on a different edge =4*[(1/4)^2]*(3/4) = 3/16 Probability dots lie on distinct edges = 4*(1/4)(3/4)(2/4) = 6/16 These 3 events only sum up to 10/16.
What are the odds of rolling a 1 or a 5 with two dice?
Hence the probability that at least one shows a 1 or 5 is 1−(2/3)2=5/9.