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...

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.