Question

Two dice are rolled.What is the probability of getting the numbers whose sum is 5 or their difference is 1?

Answer 1

@ganeshie8

Answer 2

A=getting whose sum is 5
={1,2,3,4}
B=getting their difference is 1
={1,2,3,4,5,6}

Answer 3

is correct?

Answer 4

A=getting whose sum is 5
```
1+4
2+3
3+2
4+1
```

Answer 5

ok

Answer 6

Let's find the number of ways for

B=getting their difference is 1

Answer 7

aite
it would be..
2-1
3-2
4-3
5-4
6-5

Answer 8

I think so

Answer 9

ok

Answer 10

What must we do next ?

Answer 11

Pairs, with the difference being 1:
5,6
4,5
5,4
4,3
3,4
3,2
2,3
2,1
1,2

Answer 12

and 6,5

Answer 13

Ahh nice, I think it makes more sense to include above

Answer 14

Yes :)

Answer 15

aite
it would be..
2-1
3-2
4-3
5-4
6-5

Answer 16

simply swap the number in your list :
1-2
2-3
3-4
4-5
5-6

Answer 17

ok..

Answer 18

How many outcomes are in our favor ?

Answer 19

12

Answer 20

I thought we had 10+4 = 14.
How did you get 12 ?

Answer 21

xD
Counted wrongly..
yep
B=10 and A=4

Answer 22

Careful with the duplicates in A and B
We mustn't count the same outcome twice

Answer 23

alright

Answer 24

A = { (1, 4), (2, 3), (3, 2), (4, 1)}

B = {(2, 1), (3, 2), (4, 3), (5, 4), (6, 5), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

Answer 25

A = { (1, 4), \(\color{red}{(2, 3), (3, 2)}\), (4, 1)}

B = {(2, 1), \(\color{red}{(3, 2)}\), (4, 3), (5, 4), (6, 5), (1, 2), \(\color{red}{(2, 3)}\), (3, 4), (4, 5), (5, 6)}

Answer 26

A has 4 elements
B has 10 elements
Both have 2 elements in common

Answer 27

yes

Answer 28

So total number of distinct elements = ?

Answer 29

12

Answer 30

How ?

Answer 31

14-2

Answer 32

12 was right, I'm just asking how you worked it

Answer 33

bcoz it has 2 common

Answer 34

Yes!
\[n(A ~\cup~ B) = n(A) + n(B) - n(A ~\cap ~B)\]

Answer 35

In words :

(number of elements in A or B) = (number of elements in A) + (number of elements in B) - (number of elements in both A and B)

Answer 36

12 is the number of outcomes in favor

Answer 37

rest should be easy ?

Answer 38

yes.

Answer 39

P(A)=1/3
P(B)=5/6
P(A and B)=1/6

Answer 40

Hey we don't have to calculate the individual probabilities

Answer 41

You have number of outcomes in favor (12)
You knew the total number of outcomes (36)

simply divide and you're done!

Answer 42

1/3
Thank you @ganeshie8 ^_^

Answer 43

Alternatively, you could also find the individual probabilties

Answer 44

A=getting whose sum is 5

B=getting their difference is 1


P(A) = ?

P(B) = ?

Answer 45

\[P(A)=\frac{ 4 }{ 36 }\]

Answer 46

Yes

Answer 47

P(B)=10/36=5/18

Answer 48

P(A and B)=2/36

Answer 49

Yes!

P(A or B) = P(A) + P(B) - P(A and B)

Answer 50

plugin the numbers and you should get the same answer

Answer 51

yep,i'm getting 1/3 by using that formula.. ^
Thanks again @ganeshie8 :)

Answer 52

Np :)