Probability

A red and a green dice are rolled. 

What's the probability that the sum of the pips on the top face is 5 or showing number greater than 3 ? 

This is usually the best way to do 2 dice questions - you will always see a pattern emerge.

There are 27 possibilities that have a number greater than 3 They are red.

There are 4 that add to 5 they are highlighted in yellow.

There are 2 that are in both groups.  You do not want to add those twice.

So number of possibilities is      27+4 -2 = 29

So the probability that the sum of the pips on the top face is 5 or at least one of the numbers is greater than 3 is    

                   \(\frac{29}{36}\)

Since there are 6 side on each die, and you are rolling two, there are 36 possibilities (6 faces*6 faces).

You can roll a sum of 5 with:

1, 4

2, 3

3, 2

4, 1

There are 4 ways.

That means 4 out of the 36 ways you can roll two dice (1/9 once rounded). That means there is a 1/9 chance of rolling a total of 5.

As for rolling a number greater than 3, you can roll 4, 5, or 6 on each die, which means there are 6 ways to roll two dice and get a number greater than 3 on at least one. This means that there is a 6/36 (1/6 once rounded) chance to do the same.

In conclusion, there is a 1/9 chance of getting a total of 5 and a 1/6 chance of rolling at least one number greater than 3 when rolling two dice.

Hello, 

Actually I think you did not get the question 

He's asking about both event at the same time ? So youc an't answer 1/6 and 1/9 

You ahve to compounded them. 

There is 4 chance out of 36 for the 5 

and then you have to had the solution for 3 

There is 1 chance out of 36 so there is 5 chance ot ouf 36 if I do not make any mistakes ? 

Let  P(F)  = the probability that the sum of the pips on the top face = 5

This is = 4/36   =  1/9

Let P(G)  = the probability that a number greater than a three is rolled.  This is the same probability that  1 - [a number 3 or less is rolled]  = 1- [ probability that a 2 is rolled + probability that a 3 is rolled] = 1 - [ 1/36 + 2/36]  = 36/36 - [ 3/36]  =  33/36  = 11/12

So

The probability that F or G occurs  =

P( F or G)   =

P(F) + P(G)  - P(F and G) =

(1/9) +  (33/36)  -  [ (1/9)(11/12)]  =

(4/36) + (33/36) - [ 11/108]  =

(12/108) + (99/108) - (11/108)  =

100/108 =

25/27

Oh! Thanks, Guest! I didn't see it that way!

If what you're saying is correct, then, then your work would be righ. The events' probabilities are 1/6 and 1/9, and multiplying them would result in the probability of both events occurring. 1/6*1/9=1/36,  which means that the probability of the sum of the top faces being 5 AND at least one number greater than 3 being rolled is 1/36.

However, there is a chance that the probability of either one happening was asked, and in that case, CPhill nailed it!