## Khlara Group Title A class has 3 Teaching Assistants (TAs). Each TA tosses a coin 10 times. Find the chance that at least one of the TAs gets exactly 5 heads. unanswered one year ago one year ago

1. dan815 Group Title

or in other words what is the probability when no TA gets 5 heads

2. dan815 Group Title

@FibonacciChick666 help us with this

3. FibonacciChick666 Group Title

k so lets make a chart with the outcomes

4. FibonacciChick666 Group Title

strike that cause it will take forever ok what is the probability that 1 TA will get exactly 5 heads?

5. dan815 Group Title

im thinking its like this for 1 TA

6. dan815 Group Title

7. FibonacciChick666 Group Title

hmm let me think.... ughh I'm so annoyed we did this in 6th grade why can't I remember...

8. FibonacciChick666 Group Title

at least not all 3 duh ok

9. FibonacciChick666 Group Title

ok so you would think that it would be more likely right

10. dan815 Group Title

hmm

11. FibonacciChick666 Group Title

but coins are weird because the prob for hhhhhh= prob for tthhtt

12. dan815 Group Title

is itt like this

13. dan815 Group Title

for 1 TA getting 5 heads

14. dan815 Group Title

|dw:1367217339549:dw|

15. FibonacciChick666 Group Title

i'm thinking $the~probability~for~1~TA~is~ (\frac{1}{2})^5$because they have to be in a row

16. dan815 Group Title

but it says they just need to get 5 outta 10

17. FibonacciChick666 Group Title

oh shoot hmm well that would be one half to the 10th that tells us the total combinations

18. FibonacciChick666 Group Title

then we take out anything that has more than 4 tails

19. FibonacciChick666 Group Title

5*

20. FibonacciChick666 Group Title

but we need permutations don't we

21. dan815 Group Title

i think u are right (1/2)^5 for 1 TA

22. FibonacciChick666 Group Title

if that is right then if we cubed it that would be for all three to get it but if we added them that would be for 1 right?

23. dan815 Group Title

that (1/2)^5 * 3 for 1 of the 3 having 5 heads gotta add the probability of 2 of them getting 5 heads and 3 getting 5 heads so + [(1/2^5)^2] *3 + [(1/2^5)^3]

24. dan815 Group Title

yeah all probability gotta equal 1

25. FibonacciChick666 Group Title

can't equal one

26. dan815 Group Title

im not sure though if the probability shud be 1/2^5

27. FibonacciChick666 Group Title

neither am I let me call in @hero

28. dan815 Group Title

does that look right for a dice if that is right then i guess u can just use that way for the coin too

29. FibonacciChick666 Group Title

ok... hmm that looks right but i'm just not sure it's been so long since i've taken prob and stats

30. FibonacciChick666 Group Title

you need to learn to write in LaTex...

31. dan815 Group Title

what is that

32. FibonacciChick666 Group Title

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) you can learn it here

33. FibonacciChick666 Group Title

but pretty much $you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5\$

34. FibonacciChick666 Group Title

$you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5$

35. dan815 Group Title

do you just type that out or use Equation button down there

36. FibonacciChick666 Group Title

type it out

37. dan815 Group Title

o wow lol

38. FibonacciChick666 Group Title

it is a free program for writing in math

39. FibonacciChick666 Group Title

but that is the same as using the eq button down there

40. dan815 Group Title

hbey I THINK I GOT IT NOW

41. FibonacciChick666 Group Title

sweet

42. dan815 Group Title

|dw:1367219586841:dw|

43. FibonacciChick666 Group Title

the answer cant be one...

44. dan815 Group Title

|dw:1367219732506:dw|

45. dan815 Group Title

no mean 1 - whatever that is equal to is our answer

46. FibonacciChick666 Group Title

ohhhhh uhm maybe i honestly stopped thinking about it

47. dan815 Group Title

i think iam addicted to these questions, i cant stop till i solve when someone asks these questions lol its gonna bug me for ever

48. FibonacciChick666 Group Title

i know but it's 3 am here...

49. dan815 Group Title

so are u on summer vacaation yet

50. FibonacciChick666 Group Title

yep :) for 2 weeks then summer classes you?

51. dan815 Group Title

nice, i got time till summer classes, my summer classes is in 2nd term of summer dunno when that is

52. FibonacciChick666 Group Title

lucky i have like 28 credits over the summer :/

53. dan815 Group Title

wow u took way too much in summer lol

54. dan815 Group Title

how are u gonna keep up! is ur summer term as long as the regular term

55. FibonacciChick666 Group Title

uhm kind of.... i'm not sure though cause i also work like 35 hours a week

56. dan815 Group Title

i dont think id be able to do it, unless its like all electives

57. dan815 Group Title

even then its gotta be some super easy BS on exam electives

58. FibonacciChick666 Group Title

i have PDE, single variable calc proofs, a linguistics intro course, an art class, cog. psych, and more that i forget lol

59. dan815 Group Title

oo PDE :)

60. dan815 Group Title

MATH MAJOR

61. FibonacciChick666 Group Title

ohhh yea should be fun

62. dan815 Group Title

we did some PDE toward the end of this year but i dont think its like indepth as ur PDE class

63. FibonacciChick666 Group Title

yep haha and in the fall i have abstract algebra, ODE, topology or something (math elective) ASL 3 uhmmmand something else haha

64. FibonacciChick666 Group Title

and prob not this class is going to suck massively

65. dan815 Group Title

its gonna be like that Heat equation wave equation and laplace right then using fourier series to solve?

66. dan815 Group Title

thats as far as we got, just doing simple boundary value problems with that

67. FibonacciChick666 Group Title

... were you following me on here tonight? lol

68. dan815 Group Title

whaatt do u mean

69. FibonacciChick666 Group Title

i just answered a PDE on here earlier lol

70. dan815 Group Title

oh haha

71. dan815 Group Title

i just had to cram all that stuff for my exam a couple days ago T_T

72. FibonacciChick666 Group Title

yucky

73. dan815 Group Title

it was a feather trying to learn fourier series and PDE in 2 days, I was actually gonna give up on the exam.. i went to my mom and was like NO MORE!! I WILL take this in summer

74. dan815 Group Title

but she gave me this huge LECTURE ON stick it out, just believe GOD

75. FibonacciChick666 Group Title

I had linear algebra personally but that sounds dreadful which class?

76. FibonacciChick666 Group Title

...math gods?

77. dan815 Group Title

lol

78. FibonacciChick666 Group Title

I know I usually pray to bolzano or laplace hbu? haha

79. dan815 Group Title

lmao, just Jesus for me :)

80. FibonacciChick666 Group Title

ok if that works for ya haha

81. dan815 Group Title

it dooess!! we seen too much to not believe in god

82. dan815 Group Title

i actually used to be a drug addict and stuff, till I heard God, and my addictions everything even coffee addiction i dunno how lol, just went away over night

83. dan815 Group Title

like my addictions were really really bad, i cudnt control it i cudnt get throught out a day if i wasnt high, not even 5 - 10 mins xD

84. FibonacciChick666 Group Title

thats cool for you and i'm happy you are no longer an addict

85. dan815 Group Title

yep :)

86. FibonacciChick666 Group Title

i am still a firm believer in skepticism however

87. dan815 Group Title

haha thats fine, i wud have never believed it till it finally happened to me

88. FibonacciChick666 Group Title

I was raised wayyyy too catholic, then I started thinking on my own and yep. that is how i am where i am now

89. dan815 Group Title

thats cool

90. FibonacciChick666 Group Title

but oh well, differences aside i think i'm heading to sleep/work so i'll talk to ya again soon and I'll answer this later today when I've slept a little haha

91. dan815 Group Title

okay good night sleep well :)

92. FibonacciChick666 Group Title

Night! and you too!

93. dan815 Group Title

love you lol..

94. dan815 Group Title

saying good night is a very touchy time i feel

95. NadiaKamal Group Title

HEY THIS IS THE RIGHT ANSWER

96. NadiaKamal Group Title

he probability of getting 5 heads in 10 tosses =10C5(1/2^5)(1/2^5)=252/1024=0.2461.SIMILARLY the probability of not getting five heads=1-0.2461=0.7539. now the probability of three students not getting 5 heads =(0.7539)^3=0.4285 so at last the probability of atleast one student get exactly five heads =1-0.4285 which is 0.5715

97. dan815 Group Title

98. dan815 Group Title

|dw:1367222891831:dw|

99. dan815 Group Title

|dw:1367222963861:dw|

100. dan815 Group Title

that is the probability for 1 TA getting 5 outta 10 flips as heads so for atleast 1, or otherwise, inpreted as when none of the TAs get 5 outta 10 = 1-(10 choose 5/2^10) ^3= prob of all 3 TA not getting 5 in a row so 1- prob of all 3 TA not getting 5 in a row = answer

101. KABRIC Group Title

THX

102. KABRIC Group Title

BOTH NADIA AND DAN THX

103. dan815 Group Title

YW:)