Question

What is the probability of getting a sum less than 11 when a pair of dice are rolled ?

Answer 1

@mathway can you help me ?

Answer 2

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=?

Answer 3

I'm confused !!! @surjithayer

Answer 4

What fraction I'm I multiplying ?

Answer 5

@mathstudent55 do u mind helping me out ?

Answer 6

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?

Answer 7

There 6 outcomes

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Kk I got it

Answer 13

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.

Answer 14

& how would I do that ?

Answer 15

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.

\(11, 12, 13, 14, 15, 16 \)
\(21, 22, 23, 24, 25, 26 \)
\(31, 32, 33, 34, 35, 36 \)
\(41, 42, 43, 44, 45, 46 \)
\(51, 51, 53, 54, 55, \color{red}{56} \)
\(61, 62, 63, 64, \color{red}{65}, \color{red}{66}\)

Answer 16

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

Answer 17

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

Answer 18

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

\(p(less~ than~ 11) = \dfrac{33}{36} \)

Answer 19

Correct.
Now you need to reduce 33/36.

Answer 20

Which is 11/12 ?

Answer 21

Correct.

Answer 22

Kk once again thanks I appreciate it :) @mathstudent55

Answer 23

You're welcome.

Answer 24

\[1-\frac{ 1 }{ 12 }=\frac{ 12-1 }{ 12 }=\frac{ 11 }{ 12 }\]