Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3?

7/10

3/10

5/6

3/4

9/10

Question

Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3?

7/10

3/10

5/6

3/4

9/10

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

we are given that the sum is NOT more than 5
so this is our sample space

how many ways can you get a sum NOT more than 5 ?

ganeshie8 · Answer

the sum can be 2, 3, 4 or 5, yes ?

anonymous · Answer

yes

ganeshie8 · Answer

how many ways can you get a sum of 2 ?

anonymous · Answer

one way?

ganeshie8 · Answer

yes, 

```
sum = 2  (1 way)
```

ganeshie8 · Answer

what about the sum of 3, 
how many ways ?

anonymous · Answer

one way??

ganeshie8 · Answer

you can have : 
1 + 2
or 
2 + 1

so two ways right

anonymous · Answer

ohh right, i didn't think you could count both

anonymous · Answer

ways

ganeshie8 · Answer

ok good, 

```
sum = 2  (1 way)
sum = 3  (2 way)
```

ganeshie8 · Answer

what about sum = 4, how many ways ?

anonymous · Answer

3? 2+2, 3+1, 1+3

ganeshie8 · Answer

Very good :

1 + 3 = 4
2 + 2 = 4
3 + 1 = 4

ganeshie8 · Answer

so we have 

```
sum = 2  (1 way)
sum = 3  (2 way)
sum = 4  (3 way)

```

ganeshie8 · Answer

can you guess how many ways there will be for getting a sum of 5 ?

anonymous · Answer

4?

ganeshie8 · Answer

thats it, we're almost done


```
sum = 2  (1 way)
sum = 3  (2 way)
sum = 4  (3 way)
sum = 5  (4 way)

```

ganeshie8 · Answer

so how many total ways are there for getting a sum NOT more than 5 ?

anonymous · Answer

3 ways?

anonymous · Answer

oh wait...4?

ganeshie8 · Answer

nope, just add them up : 1+2+3+4 = ?

anonymous · Answer

10!

ganeshie8 · Answer

Yes!
how many of them have sum more than 3 ?

anonymous · Answer

6?

ganeshie8 · Answer

how ?

ganeshie8 · Answer

just look at the table that we have created earlier

```
sum = 2  (1 way)
sum = 3  (2 way)
sum = 4  (3 way)
sum = 5  (4 way)

```

ganeshie8 · Answer

simply add the number of ways that we can get sum of 4 and 5

anonymous · Answer

2?

ganeshie8 · Answer

how ?

anonymous · Answer

im sorry! i suck

ganeshie8 · Answer

sum = 2  (1 way)
sum = 3  (2 way)
`sum = 4  (3 way)`
`sum = 5  (4 way)`

add them : 3+4 = 7 ways

ganeshie8 · Answer

outcomes in favor = 7
total outcomes = 10

probability = ?

anonymous · Answer

right...im so stupid 
7/10

ganeshie8 · Answer

you're not stupid, you're doing great!
thest things takes practice

anonymous · Answer

thank you! no wonder you have so many fans! haha

ganeshie8 · Answer

haha that is because i have been here so long
yw :)