Question

Two number cubes are rolled for two separate events:

All of the combinations of numbers on both cubes that give a sum less than 10.
All combinations of numbers on both cubes that give a sum that is a multiple of 3.

In terms of a reduced fraction, find the conditional probability of B given that A occurs first.

Answer 1

Any idea? Can you draw out the sample ?

Answer 2

@jim_thompson5910

Answer 3

how far did you get @desmarie ?

Answer 4

not very far :/

Answer 5

were you able to get started at all?

Answer 6

if so, post what you got so far

Answer 7

if not then that's ok just let me know

Answer 8

I saw something online but it just confused me more

Answer 9

So I'm assuming

event A = All of the combinations of numbers on both cubes that give a sum less than 10.

event B = All combinations of numbers on both cubes that give a sum that is a multiple of 3.

are these assumptions correct?

Answer 10

or does your book not say which events are which?

Answer 11

that is correct

Answer 12

they had them in that order

Answer 13

" In terms of a reduced fraction, find the conditional probability of B given that A occurs first. "

so we're told that event A occurs first. So we are guaranteed 100% that event A happens.

This means whatever was rolled, it was a sum less than 10

let's start with a chart like this

see attached

Answer 14

let's go through the chart and mark all the boxes that have a sum less than 10

I'm going to use light blue to mark the boxes

Answer 15

do you agree with how I marked up the table?

Answer 16

so it would not be just the numbers that add up to 10.....I thought it would be just the numbers up to 5

Answer 17

I'm not sure what you mean

Answer 18

the numbers that have a sum less than 10.... for example the sum of nine and eight is more than ten so....

Answer 19

9 isn't on the number cube though. A common number cube goes from 1 to 6

Answer 20

the cells I marked in blue are the sums of the two dice

for instance, 2nd column in the bottom row is 6+2 = 8

die1 = 6
die2 = 2
sum of dice = 8

it is marked blue because 8 is less than 10

Answer 21

lol....it is cause I saw the nine highlited......I feel so embarrased

Answer 22

ok so yeah I agree with how you marked up the table

Answer 23

ok so what we do is focus on just the blue cells

ignore the other cells (ignore 10, 11, and 12)

ignore the values that line the left or top

Answer 24

how many values are marked in blue?

Answer 25

6 right

Answer 26

way more than 6

Answer 27

count again

http://assets.openstudy.com/updates/attachments/574df5e8e4b098f70ee17a1b-jim_thompson5910-1464739950672-dice_chart2.png

Answer 28

30??

Answer 29

yep 30 blue boxes

Answer 30

how many of these blue boxes have values that are multiples of 3?

multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, ....

Answer 31

11?

Answer 32

yep there are 11 green boxes

the green boxes are multiples of 3 AND values less than 10

Answer 33

so we have 11 green boxes

out of 30 total blue boxes

Answer 34

so we just divide the values at this point

11/30

the probability of getting a multiple of 3 given the sum is less than 10 is 11/30

Answer 35

posssible events are