## anonymous one year ago 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)

1. anonymous

1 is .25 do you know why?

2. anonymous

2 is 1/36

3. anonymous

no

4. anonymous

no sorry 7/36

5. anonymous

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

6. anonymous

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

7. anonymous

there like 2 dice(6*6=36)

8. anonymous

i see, so is 1/4

9. anonymous

$\frac{ 3 }{ 6 } \times \frac{ 3 }{ 6 }=?$

10. anonymous

yea

11. anonymous

that solve the first part, is 1/4

12. anonymous

yea but i would use decimals unless it asks for fractions

13. anonymous

k

14. anonymous

ok so #2

15. anonymous

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

16. anonymous

so 7/36 would be the probability

17. anonymous

k

18. anonymous

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

19. anonymous

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

20. anonymous

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

21. anonymous

16/36?

22. anonymous

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

23. anonymous

so?

24. anonymous

ya u are right

25. anonymous

{1,7} , so on

26. anonymous

yea

27. anonymous

ok so #2 is?

28. anonymous

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

29. anonymous

^^^^^

30. anonymous

but its 6 not 5 because th 4,4 repeats

31. anonymous

that solve second question

32. anonymous

yea

33. anonymous

correct.6/36

34. anonymous

so #3 do you know what to do??

35. anonymous

finding a numbers that is less that 7

36. anonymous

yea but combos like {1,5} so on

37. anonymous

but not =7 its <7

38. anonymous

ya i notice that

39. anonymous

12/36

40. anonymous

try again

41. 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

42. anonymous

try to make a diagram or draw it

43. anonymous

44. anonymous

i miss some numbers

45. anonymous

|dw:1444443620290:dw|

46. anonymous

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

47. anonymous

so there is 15 total

48. anonymous

49. anonymous

not 30

50. anonymous

well actualy no thats right it repeats

51. anonymous

so yea 30/36

52. anonymous

now part 4

53. anonymous

same thing just draw it out

54. anonymous

is 30/36 ?

55. anonymous

12/36 or

56. anonymous

4) is 7/6 5) 7/36

57. anonymous

sorry is 10/36 for the last part

58. 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?

59. anonymous

i just simplify the number 16/36

60. 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

61. anonymous

ya is 21/36 i guess i miss some calculation