Question

Two dice are rolled simultaneously. What is the probability that the product of the two dice is a multiple of 6?

Answer 1

How do I solve for it step by step?

Answer 2

multiples of 6, between 6 and 36 are:
6, 12, 18, 24, 30, 36
so 6 possible answers

Answer 3

list out all possible ways to get 6, 12, 18, 24, 30 or 36 by multiplying together the two numbers.
the number of possible ways divided by the 36 (do you see why?) is the probability.

Answer 4

So is the probability 5/12?

Answer 5

@Peter14's idea is correct, but be sure to think of the two die as different color (say, red and green) because a R1 and a G6 is a different roll than a G1 and R6.

Answer 6

so for 1 die
6 and anything (6)
5 and 6 (1)
4 and 6 or 3 (2)
3 and any even number (3)
2 and 3 or 6 (2)
1 and 6 (1)

Answer 7

here, i'll give you one example: all possible ways to get 6: g1*r6, g2*r3, g3*r2, g6*r1

Answer 8

Jack I'm just a little worried that you're counting the same rolls twice with that first group of (6) and the ones below it.

Answer 9

jack's way is the one you come up with when you can do it intuitively, my way is the procedural way

Answer 10

@zepdrix i think you're right

Answer 11

I don't think jack's way is wrong... let's see.

Answer 12

@danielle02

you are correct

Answer 13

it is wrong...it double counts the 6/1 combination...i actually get 16/36 = 4/9. did i miss some combinations?

Answer 14

but you should double count 6/1 because you can get 6/1 and 1/6

Answer 15

the only one you don't double count is 6/6

Answer 16

but he was only looking at a single die's values.

Answer 17

(1,6)
(2,6)
(3,6)
(4,6)
(5,6)
(6,6)
(6,5)
(6,4)
(6,3)
(6,2)
(6,1)
(2,3)
(3,2)
(2,4)
(4,2)

Answer 18

6/6 shouldn't be doubled because it is the same as itself

Answer 19

(3,4)
(4,3)

Answer 20

@zrkon, why didn't you double count 6/6

Answer 21

not(2,4)(4,2)

Answer 22

there is only one way to get (6,6) you get a 6 and a 6 ;)

Answer 23

but the dice are each independent. otherwise there'd be 35 possible combinations total

Answer 24

Ahh i counted (6,6) twice :)

No wonder I was getting 16 lol

Answer 25

so if the rest was right, 14=14 =28/36 = 7/9...?

Answer 26

tht's why you think of them as different colors

Answer 27

15/36=5/12

Answer 28

so guys, what are we arguing about now?

Answer 29

@Zarkon that just seems a little low...?

Answer 30

it is what it is

Answer 31

jack, you don't multiply it by 2

Answer 32

thanks guys

Answer 33

what about 3,4 and 4,3...?

Answer 34

shouldnt that make it 17/36...?

Answer 35

if you want to do it your way, do it like this
stem and leaf plot
6 | 123456
5 | 6
4 | 36
3 | 246
2 | 36
1 | 6
count the total number of leaves, and that's your number over 36

Answer 36

apparently it's too early for me to do probability :P ignore my 6/6 discussion above :D

Answer 37

you see I have covered every way to multiply to get a multiple of 6...

Answer 38

(1,6)
(2,3)
(2,4)
(2,6)
(3,6)
(3,2)
(3,4)
(4,6)
(4,3)
(4,2)
(5,6)
(6,6)
(6,5)
(6,4)
(6,3)
(6,2)
(6,1)
... this is the list of combo's... yeah?

Answer 39

and there are 17...?

Answer 40

2,4 and 4,2 don't work...product is 8

Answer 41

ah ha , lol my bad