Question

You roll 2 dice. What is the probability that the sum of the dice is greater than 8 and that 1 die shows a 6?

Answer 1

how many outcomes are favorable to us?

Answer 2

to get a 6 is 2/6 to get greater than 8 is 23/36 i think

Answer 3

lets do cases

case1:

roll a 6, then roll a 3,4,5,6 seems reasonable

how do we define this probability?

Answer 4

is this the npn

Answer 5

no, this is just counting rule basically

Answer 6

we have 1 way to roll a 6 first, we have 4 ways to win afterwards

1*4 = 4, out of 36 possible outcomes agreed? thats case 1

Answer 7

case2:

we have 4 ways to roll (3,4,5,6), and afterwards we have only 1 way to win (roll a 6)

4*1 = 4, out of 36 possible outcomes

Answer 8

i thought we did 6*4

Answer 9

no, 6 is the name of a face, not the number of times it happens

Answer 10

spose we had dice with faces: a,b,c,d,e,f

whats the probability of rolling an 'a', and then either (c,d,e,f) ?

Answer 11

a= 1/6 then 4/6

Answer 12

then P(a and P(c or d or e or f)) =

P(a) * P(c or d or e or f)

1/6 * 4/6 agreed?

Answer 13

and of course case2:

P(c or d or e or f) and P(a) would be

4/6 * 1/6

the sum of case 1 and case 2 is the total probability of our desired outcomes

Answer 14

so i add them so for mine is 1/6 then 1/2 = 2/3

Answer 15

\[\left[ \begin{array}c & 1 & 2 & 3 & 4 & 5 & 6\\1 & 11 & 12 & 13 & 14 & 15 & 16\\2 & 21 & 22 & 23 & 24 & 25 & 26\\3 & 31 & 32 & 33 & 34 & 35 & \color{red}{36}\\4 & 41 & 42 & 43 & 44 & 45 & \color{red}{46}\\5 & 51 & 52 & 53 & 54 & 55 & \color{red}{56}\\6 & 61 & 62 & \color{red}{63} & \color{red}{64} & \color{red}{65} & \color{red}{66}\\\end{array} \right]\]

since one case is common to both ... 7 out of 36 is what i see

Answer 16

how

Answer 17

i dont get math. i use to be good but now i dont know

Answer 18

i really cant do better than the picture of outcomes ....

Answer 19

we have 7 possible results, i colored them red

we have 36 possible outcomes in all

probability is defined as:

#favored outcomes
----------------
#total outcomes

Answer 20

in my table is
123456
1234567

Answer 21

\[\frac{4}{36}+\frac4{36}-\frac1{36}=\frac7{36}\]
we are counting 1/36 twice (its common to both cases) so we get an overcount of 1 ... have to subtract it to get back in line.

Answer 22

and your table is
123456
1111213

Answer 23

36 isnt the number 36, its the roll (3 then a 6)

Answer 24

36 sums to 9

Answer 25

now i get it

Answer 26

:)

Answer 27

i kept them seperated simply to see which roles have a 6 in them, and a (3,4,5,6) as well

Answer 28

so is not 36 is 3 and 6
then 4 and 6 and so on

Answer 29

correct