Experiment consists if rolling a pair dice and observing the numbers that falls uppermost on each side. many ways can you obtain each result?

Question

1) a 5 on at least one of the dice.

2) a sum of at least 4

Answer 1

To get a "5" on at least one die, the probability is 11/36. This can be seen as 1 - p(no five on two dice). Now, the probability that the first die is not a "5" is 5/6. This is also true for the second die. The probability that neither the first nor the second is a "5" is the product 5/6 * 5/6 = 25/36. Then 1 - 25/36 = 11/36.

 

I agree that the probability that the sum of two dice must be at least 4 is 33/36 or 11/12 when reduced. James gave the correct answer for that part, but I needed to respond since he got the first part wrong.

 

 

Answer 2

If the question is how many ways can these results happen:

 

1) Only 2 ways - a 5 on one die, or a 5 on the other.

 

2) There are only three ways to get a sum of less than 4.

1-1

1-2

2-1

 

Therefore, the answer is the total number of combinations on 2 dice minus three.

 

There are 36 possible combinations.

 

So the answer is 33.

 

Hope this helps, Julio!