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Lecture 13

# AMS 5 Lecture 13: Class 13 - Probability: On Coin Tosses Premium

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Department
Applied Math and Statistics
Course
AMS 5
Professor
Yonatan Katznelson
Semester
Spring

Description
AMS 5 Lecture 13 552017 (8:009:05) Coin Tosses If a fair coin is tossed 10 times, what will we see? o The probability of HHHHHHHHHH and HTTHHTTHTH occurring in that order are the same; P(HHHHHHHHHH) = P(HTTHHTTHTH) = ^10 = 11024 o of sequences = 1024 o of sequences with 10 H = 1 o of different sequences with 5 H = 252 P(5 H in 10 tosses) = 2521024 = 63251 ~ 24.6 o of sequences with 2 H and 8 T = (10 2)10C 2 10.92 = 45 Number of H in ten tosses 0 .098 1 .98 2 4.39 3 11.72 4 20.51 5 24.61 6 20.51 7 11.72 8 4.39 9 .98 10 .098 Observations o The probability of seeing exactly 5 H in 10 tosses is just below 25 o The probability that the number of H is between 4 and 6 is close to 66 o The probability that the number of H is between 3 and 7 is about 89 o We could summarize the se s by saying that we will probably see o Even if you were to toss the coin 100 times, the percentages would be mostly the same.
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