Q: Corbin is playing a board game that requires rolling two number cubes to move a game piece. He needs to roll a sum of six on his next term and then a sum of ten to land on to the next two bonus spaces. what is the probability that Corbin will roll a sum of six and then a sum of ten on his next two turns?
Will someone please help me with this because I have spent a long time trying to find the answer to this question but I have no idea how to find the answer or even know how to solve it, so can someone please help me with this question and can someone please help explain how to solve this question???
THANK YOU :D
help me.....
The probability of rolling a six with two dice is 5/36. The probability of rolling a ten with two dice is 3/36 = 1/12. You should be able to convince yourself of this. If not, read
http://wizardofodds.com/gambling/dice/
The probability of rolling six followed by ten is the product of those two numbers, 5/432.
To find the probability of rolling a sum of six and then a sum of ten on his next two turns, we first need to determine the total number of outcomes for each roll.
On each roll, the number cube can land on any number from 1 to 6. Since there are two number cubes, the total number of outcomes for each roll is 6 x 6 = 36.
To calculate the probability of getting a sum of six on the first roll, we need to determine how many ways we can get a pair of numbers that add up to six. These pairs are (1, 5), (2, 4), and (3, 3). So, there are three possible outcomes out of 36 total outcomes, giving a probability of 3/36 or 1/12.
Similarly, to calculate the probability of getting a sum of ten on the second roll, we need to determine how many ways we can get a pair of numbers that add up to ten. These pairs are (4, 6) and (5, 5). So, there are two possible outcomes out of 36 total outcomes, giving a probability of 2/36 or 1/18.
To find the probability of both events happening, we multiply the probabilities of each event occurring. So,
Probability of rolling a sum of six and then a sum of ten = Probability of rolling a sum of six * Probability of rolling a sum of ten
= (1/12) * (1/18)
= 1/216
Therefore, the probability that Corbin will roll a sum of six and then a sum of ten on his next two turns is 1/216.
To find the probability that Corbin will roll a sum of six and then a sum of ten on his next two turns, we need to consider the possible outcomes of rolling two number cubes.
Let's start by understanding the possible outcomes when rolling two number cubes. Each cube has six sides with numbers 1, 2, 3, 4, 5, and 6. When two cubes are rolled, all possible combinations can be found by multiplying the number of sides on each cube. In this case, there are a total of 6 x 6 = 36 possible outcomes.
Next, we need to determine the number of outcomes that result in a sum of six on the first turn. These outcomes can be expressed as pairs of numbers (a, b) where a + b = 6. The pairs that satisfy this condition are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). So there are five possible outcomes that result in a sum of six on the first turn.
Similarly, we need to determine the number of outcomes that result in a sum of ten on the second turn. The pairs that satisfy the condition a + b = 10 are (4, 6), (5, 5), and (6, 4). So there are three possible outcomes that result in a sum of ten on the second turn.
To find the probability of both events occurring, we multiply the probabilities of each event happening separately. The probability of rolling a sum of six on the first turn is 5/36 (since there are 5 favorable outcomes out of 36 possible outcomes). The probability of rolling a sum of ten on the second turn is 3/36.
Multiplying these probabilities together, we get:
(5/36) * (3/36) = 15/1296
So the probability that Corbin will roll a sum of six and then a sum of ten on his next two turns is 15/1296, or approximately 0.0116, which can be rounded to 0.01 or 1%.