Question

Please help for medal and fan and just to be nice (:
Suppose you roll two number cubes and find the probability distribution for the sum of the numbers. Which two sums have the same probability distribution and would be represented with equal bars on a bar graph?
A. 4 and 11
B. 6 and 9
C. 5 and 10
D. 2 and 12

Answer 1

well "7" is most likely, then its a symmetric distribution...
6 same as 8
5 same as 9
and so on...

Answer 2

wait i dont understand...what would the answer be then?

Answer 3

fill in the table, and you will see the number of ways to get each roll

Answer 4

do i fill it in by multiplying the two dice or adding them?

Answer 5

add

Answer 6

as you add the tops of the dice to get each total

Answer 7

and then what do i do after that?

Answer 8

how do i know what the answer is?

Answer 9

count the number of ways to get each total
for example there are 3 ways to get a total of 4, so the probability you get a 4 is \(\frac{3}{36}\)

Answer 10

you will notice that there is only one way to get a total of 2 (namely (1,1)) and also only one way to get a total of 12 (6,6)

Answer 11

im still confused haha

Answer 12

counts the totals of how to get each number?

Answer 13

ok lets go slow

Answer 14

when you fill out the table you will see the number of ways to get each total

Answer 15

for example, there are 6 different ways to roll a total of 7
as a list they look like this:
(1,6), (2,5), (3,4) , (4,3), (5,2), (6,1)

Answer 16

there is only one way to roll a total of 2, namely (1,1) and also there is only one way to get a total of 12, namely (6,6)

Answer 17

you should see the nice pattern as suggested by @dumbcow above

Answer 18

alternative way:


as dumbcow pointed out


"well '7' is most likely, then its a symmetric distribution...
6 same as 8
5 same as 9
and so on..."


there is a trick/shortcut: if the two numbers add to 14, then the two numbers are equally likely. Notice how 7+7 = 14, 6+8 = 14, 5+9 = 14, etc


since 2+12 = 14, this means that 2 and 12 have the same probability of occurring

Answer 19

Ohhhhh okay, I just figure it out right before I read @jim_thompson5910 's answer lol thanks for all your help both of you @satellite73