Probability: Product and Addition rule confusion (1 Viewer)

[Weeber]

Hi guys,

Q: 2 Dice are thrown and their sum noted, find the probability of getting a total of 2.

Since there are 2 Dies (let's call them A and B) wouldn't the solution be P(1A,1B) or P(1B,1A)?

so (1/6 x 1/6) + (1/6 x 1/6)?

Thank you.

Answer says something else.

 

[Smile12345]

1/36... Is that what the answers say??

 

[Smile12345]

Sum is addition.

 

[RealiseNothing]

1/36... Is that what the answers say??

This, it's the probability that you throw two 1's.

 

[Smile12345]

This, it's the probability the you throw two 1's.

Thanks.

 

[Trebla]

Hi guys,

Q: 2 Dice are thrown and their sum noted, find the probability of getting a total of 2.

Since there are 2 Dies (let's call them A and B) wouldn't the solution be P(1A,1B) or P(1B,1A)?

so (1/6 x 1/6) + (1/6 x 1/6)?

Thank you.

Answer says something else.

The dice are treated as identical. When you order two identical numbers (1 + 1) then you only count it once whereas if you order two distinct numbers (say 2 and 3) then you count twice (2 + 3 and 3 + 2).

Intuitively if you think about the 1 and 1 case, each die can only roll a single particular number whereas the 2 and 3 case, each die can roll two possible numbers (2 or 3) provided the other die rolls the other number.

 

[Weeber]

Could you go through the working out please.

 

[Smile12345]

Could you go through the working out please.

This is one way to do it. Probably the most straight forward.

1. Draw up a table - 7 squares by 7 squares.

2. Leave the first square blank.

3. Then write 1 - 6 across the table and 1 - 6 down the table...

4. Then complete each addition required until you have completed the table.

i.e. going across the 2nd row.... 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4 ............... right to 6 + 6 = 12

5. Now, you have 36 answers in total .... How many of these are two (you needed the two numbers to add to 2)??

6. There is only one option (1 + 1) so we get 1/36...

 

[Weeber]

This is one way to do it. Probably the most straight forward.

1. Draw up a table - 7 squares by 7 squares.

2. Leave the first square blank.

3. Then write 1 - 6 across the table and 1 - 6 down the table...

4. Then complete each addition required until you have completed the table.

i.e. going across the 2nd row.... 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4 ............... right to 6 + 6 = 12

5. Now, you have 36 answers in total .... How many of these are two (you needed the two numbers to add to 2)??

6. There is only one option (1 + 1) so we get 1/36...

I meant using the product rule?