Two six sided dice (one is red, one is green) are rolled. Determined the following probabilities:
1)
What is the probability that the red die is even and the green die is odd? That is, P(R=even∩G=odd)
2)What is the probability that the sum of the red and green values is 8 .
3) What is the probability that the sum of the red and green values is <7 ? That is, P(R+G<7).
4) What is the probability that red value is ≤ green value? That is, P(R≤G)
5) What is the probability that red value ≤ green and the green value is <6 ? That is, P(R≤G∩G<6)

- anonymous

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- anonymous

1 is .25 do you know why?

- anonymous

2 is 1/36

- anonymous

no

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- anonymous

no sorry 7/36

- anonymous

ok for number 1 do you know that if you have two independent probabilities you multiply them to find their combined probability?

- anonymous

so the P(even dice roll)=.5 and P(odd dice roll)=.5 so .5•.5=.25

- anonymous

there like 2 dice(6*6=36)

- anonymous

i see, so is 1/4

- anonymous

\[\frac{ 3 }{ 6 } \times \frac{ 3 }{ 6 }=?\]

- anonymous

yea

- anonymous

that solve the first part, is 1/4

- anonymous

yea but i would use decimals unless it asks for fractions

- anonymous

k

- anonymous

ok so #2

- anonymous

there are 36 total combinations and only 7 add up to 8

- anonymous

so 7/36 would be the probability

- anonymous

k

- anonymous

sorry wait i didnt account for 1 so its 8/36 which can be simplified

- anonymous

1,7 2,6 3,5 4,4 4,4 5,3 6,2 1,7

- anonymous

those are the combos that add up to 8 for the red and green

- anonymous

16/36?

- anonymous

well no because there are 16 numbers but they come in pairs

- anonymous

so?

- anonymous

ya u are right

- anonymous

{1,7} , so on

- anonymous

yea

- anonymous

ok so #2 is?

- anonymous

2.
26,35,44,53,62
P=5/36

- anonymous

^^^^^

- anonymous

but its 6 not 5 because th 4,4 repeats

- anonymous

that solve second question

- anonymous

yea

- anonymous

correct.6/36

- anonymous

so #3 do you know what to do??

- anonymous

finding a numbers that is less that 7

- anonymous

yea but combos like {1,5} so on

- anonymous

but not =7 its <7

- anonymous

ya i notice that

- anonymous

12/36

- anonymous

try again

- anonymous

11,12,13,14,15,21,22,23,24,31,32,33,41,42,51first is G,second is Red
same is first Red,second is Green
P=30/36=5/6

- anonymous

try to make a diagram or draw it

- anonymous

already did

- anonymous

i miss some numbers

- anonymous

|dw:1444443620290:dw|

- anonymous

so count all the numbers under the red and thats the combo totals

- anonymous

so there is 15 total

- anonymous

indeed already saw the answer from @surjithayer

- anonymous

not 30

- anonymous

well actualy no thats right it repeats

- anonymous

so yea 30/36

- anonymous

now part 4

- anonymous

same thing just draw it out

- anonymous

is 30/36 ?

- anonymous

12/36 or

- anonymous

4) is 7/6
5) 7/36

- anonymous

sorry is 10/36 for the last part

- zepdrix

I don't quite understand your fraction for part 4.
7/6?
So you're saying the red die will be less than the green die over 100% of the time?

- anonymous

i just simplify the number 16/36

- zepdrix

Which does not simplify to 7/6...
but anyway I think maybe you missed a few, hmm
If a 1 is rolled on the red die,
and we want the green to be greater than or equal to that,
We can roll any number on the green die, ya?
If a 2 is rolled on the red die,
We can roll any number larger than a 1 on the green die.
R1 G123456
R2 G 23456
R3 G 3456
R4 G 456
R5 G 56
R6 G 6
=6+5+4+3+2+1
I think that's 21 of the 36 combinations, isn't it? :o

- anonymous

ya is 21/36 i guess i miss some calculation

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