For this one i have no idea what formula or even how to set it up...
Tow 6-sided dice are rolled. What is the porbability that the sum of the two numbers on the dice will be greater than 9?
Notation: n1 is the number that die 1 shows, n2 is the number that die 2 shows.
Then we want to know in how many ways you can have:
n1 + n2 > 9
where:
1 <= n1 <= 6
1 <= n2 <= 6
We know that without restrictions there are 36 possibilities (both n1 and n2 can then take 6 values), so we have to divide the number of possibilities by 36.
In this case the number of possibilities is not that large and you can just count all possibilities:
n1 = 4, n2 = 6
n1 = 5, n2 = 5
n1 = 5, n2 = 6
n1 = 6, n2 = 4
n1 = 6, n2 = 5
n1 = 6, n2 = 6.
by anychance do you know of a good website where it shows a similar example of how to use this type of formula....
I think the best thing you could do is study discrete mathematics from a good textbook.
I just found this PDF file:
http://www.cs.tau.ac.il/~odedr/teaching/discrete_math_fall_2005/dmbook.pdf
The probability that the sum of the numbers on two 6-sided dice will be greater than 9 can be found by counting the number of favorable outcomes and dividing by the total number of possible outcomes.
In this case, we want to find the number of ways we can have n1 + n2 > 9, where n1 and n2 are the numbers on the two dice. Since each die has 6 possible outcomes (numbers 1 to 6), there are a total of 6 * 6 = 36 possible outcomes without any restrictions.
To count the number of favorable outcomes, we need to find all the pairs (n1, n2) that satisfy the condition n1 + n2 > 9.
By listing out all the possible pairs (n1, n2), we find the following pairs that satisfy the condition:
- (4, 6)
- (5, 5)
- (5, 6)
- (6, 4)
- (6, 5)
- (6, 6)
Therefore, there are 6 favorable outcomes.
To find the probability, we divide the number of favorable outcomes (6) by the total number of possible outcomes (36):
Probability = favorable outcomes / total outcomes = 6 / 36 = 1/6
So the probability that the sum of the numbers on the two dice will be greater than 9 is 1/6.
As for finding a good website for similar examples, you can refer to the PDF file I found: http://www.cs.tau.ac.il/~odedr/teaching/discrete_math_fall_2005/dmbook.pdf It contains material on discrete mathematics which is helpful for solving problems like these.