# The chance﻿﻿Consider a fair coin tossed 100 times. a) what is the probability of landing heads 55 times or more? b) what is the chance of getting between 40 and 60 tails on the 100 flips?

hala718 | High School Teacher | (Level 1) Educator Emeritus

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a) The probability of landing head = 1/2

Since each roll is independednt, then prbability of landing heads 55 time or more = probability of landing heads 55 times + probability of landing 56 times + ...+ probability of langing heads 100 times

= (1/2)^55 + (1/2)^56 + ...+ (1/2)^100

= (1/2)^55 [ 1 + 1/2 + (1/2)^2 + ... + (1/2)^ 45]

B) Probability for getting between 40 and 6o tails = probability of getting 41 tails + P(42 tails) + ...+ P(59 tails)

= (1/2)^41 + (1/2)^42 + .... (1/2)^59)

neela | High School Teacher | (Level 3) Valedictorian

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In an unbiased coin chance of getting a head = chance of getting atail = 1/2

The probability of getting x heads in n tosses of the coin is given by

P(x) =( nCx )(1/2)^x)(1/2)^(n-x).

Since n =100, probability of getting hed s 55 or more = p(x=55)+P(x>55) = P(x > =55) = Summation P(x) for x =55 to 100.

Summation  (100Cx) ((1/2)^x) (1/2)^(100-x) = (100Cx)(1/2^100

=0.18410080866 from tables.

Probability of number of  hesds(= x ) between 40 and 60 is

P( 40 < x<60) = summation 100Cx (1/2)^100.  for x= 41, 42, 43,...60.

=  P(x <= 59) - P((x< = 40) = 0.977155 60331 - 0284439668 = 9511120662 from tables.