## Khlara 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

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

2. dan815

@FibonacciChick666 help us with this

3. FibonacciChick666

k so lets make a chart with the outcomes

4. FibonacciChick666

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

5. dan815

im thinking its like this for 1 TA

6. dan815

7. FibonacciChick666

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

8. FibonacciChick666

at least not all 3 duh ok

9. FibonacciChick666

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

10. dan815

hmm

11. FibonacciChick666

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

12. dan815

is itt like this

13. dan815

for 1 TA getting 5 heads

14. dan815

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15. FibonacciChick666

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

16. dan815

but it says they just need to get 5 outta 10

17. FibonacciChick666

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

18. FibonacciChick666

then we take out anything that has more than 4 tails

19. FibonacciChick666

5*

20. FibonacciChick666

but we need permutations don't we

21. dan815

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

22. FibonacciChick666

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

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

yeah all probability gotta equal 1

25. FibonacciChick666

can't equal one

26. dan815

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

27. FibonacciChick666

neither am I let me call in @hero

28. dan815

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

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

you need to learn to write in LaTex...

31. dan815

what is that

32. FibonacciChick666

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

33. FibonacciChick666

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

34. FibonacciChick666

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

35. dan815

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

36. FibonacciChick666

type it out

37. dan815

o wow lol

38. FibonacciChick666

it is a free program for writing in math

39. FibonacciChick666

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

40. dan815

hbey I THINK I GOT IT NOW

41. FibonacciChick666

sweet

42. dan815

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43. FibonacciChick666

44. dan815

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45. dan815

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

46. FibonacciChick666

ohhhhh uhm maybe i honestly stopped thinking about it

47. dan815

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

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

49. dan815

so are u on summer vacaation yet

50. FibonacciChick666

yep :) for 2 weeks then summer classes you?

51. dan815

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

52. FibonacciChick666

lucky i have like 28 credits over the summer :/

53. dan815

wow u took way too much in summer lol

54. dan815

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

55. FibonacciChick666

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

56. dan815

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

57. dan815

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

58. FibonacciChick666

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

59. dan815

oo PDE :)

60. dan815

MATH MAJOR

61. FibonacciChick666

ohhh yea should be fun

62. dan815

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

63. FibonacciChick666

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

64. FibonacciChick666

and prob not this class is going to suck massively

65. dan815

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

66. dan815

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

67. FibonacciChick666

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

68. dan815

whaatt do u mean

69. FibonacciChick666

i just answered a PDE on here earlier lol

70. dan815

oh haha

71. dan815

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

72. FibonacciChick666

yucky

73. dan815

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

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

75. FibonacciChick666

76. FibonacciChick666

...math gods?

77. dan815

lol

78. FibonacciChick666

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

79. dan815

lmao, just Jesus for me :)

80. FibonacciChick666

ok if that works for ya haha

81. dan815

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

82. dan815

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

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

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

85. dan815

yep :)

86. FibonacciChick666

i am still a firm believer in skepticism however

87. dan815

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

88. FibonacciChick666

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

thats cool

90. FibonacciChick666

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

okay good night sleep well :)

92. FibonacciChick666

Night! and you too!

93. dan815

love you lol..

94. dan815

saying good night is a very touchy time i feel

HEY THIS IS THE RIGHT ANSWER

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

98. dan815

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99. dan815

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100. dan815

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

THX

102. KABRIC