## anonymous one year ago What is the probability of getting a sum less than 11 when a pair of dice are rolled ?

1. anonymous

@mathway can you help me ?

2. anonymous

possible events for a sum of 11 or more than 11 are 56,65,66 no. of events=3 total no. of events=36 P(for a sum 11 or more )=3/36=1/12 P(for a sum less than 11)=1-1/12=?

3. anonymous

I'm confused !!! @surjithayer

4. anonymous

What fraction I'm I multiplying ?

5. anonymous

@mathstudent55 do u mind helping me out ?

6. mathstudent55

The probability of an event happening is the number of ways the even can happen divided by the total number of ways. When you roll 2 dice, what is the total number of outcomes?

7. anonymous

There 6 outcomes

8. mathstudent55

Below you see all possible outcomes of rolling 2 dice. How many outcomes are there? 11, 12, 13, 14, 15, 16 21, 22, 23, 24, 25, 26 31, 32, 33, 34, 35, 36 41, 42, 43, 44, 45, 46 51, 51, 53, 54, 55, 56 61, 62, 63, 64, 65, 66

9. mathstudent55

One single die has 6 outcomes, but when you roll two dice, you need to find all possible combinations of outcomes of the two.

10. anonymous

I'm guessing there are 2 I'm not sure

11. mathstudent55

Look above. Each pair of numbers is a different outcome. There are 36 possible different outcomes.

12. anonymous

Kk I got it

13. mathstudent55

When a pair of dice are rolled, there are 36 possible different outcomes. Now you need to find out how many of the 36 different outcomes have a sum less than 11.

14. anonymous

& how would I do that ?

15. mathstudent55

You add the numbers of the two dice. All outcomes in black below are less than 11. The outcomes in red are 11 or more. $$11, 12, 13, 14, 15, 16$$ $$21, 22, 23, 24, 25, 26$$ $$31, 32, 33, 34, 35, 36$$ $$41, 42, 43, 44, 45, 46$$ $$51, 51, 53, 54, 55, \color{red}{56}$$ $$61, 62, 63, 64, \color{red}{65}, \color{red}{66}$$

16. mathstudent55

Out of 36 outcomes, only 3 are 11 or more. That means 33 are less than 11.

17. anonymous

So the probability of getting a sum less than 11 when a pair of dice are rolled are 33/36?

18. mathstudent55

Now you see that your desired outcomes are 33,and the total outcomes are 36. The probability of rolling a number less than 11 is $$p(less~ than~ 11) = \dfrac{33}{36}$$

19. mathstudent55

Correct. Now you need to reduce 33/36.

20. anonymous

Which is 11/12 ?

21. mathstudent55

Correct.

22. anonymous

Kk once again thanks I appreciate it :) @mathstudent55

23. mathstudent55

You're welcome.

24. anonymous

$1-\frac{ 1 }{ 12 }=\frac{ 12-1 }{ 12 }=\frac{ 11 }{ 12 }$