Each member of a nine person committee attends any given meeting of the committee with a probability of 1/2. What is the probability that at least two-thirds of the membership of the committee will be present at its next meeting?

To solve the question we proceed as follows:

2/3 * (9) = 6

Thus the probability that at least 6 members will attend will be given by the sum of the probabilities that 6,7,8,9 members will attend the meeting.

Probability that n members will attend is given by:

9Cn=9! / ((9-n) !*n!)

thus

P (n=6) = 9! (3!6!) / 512=84/512

p (n=7) = 9! / (2!*7!) / 512=36/512

p (n=8) = 9! / (1!*8!) / 512=9/512

p (n=9) = 9! / (0!*9!) / 512=1/512

thus the probability that at least 6 members will attend is:

84/512+36/512+9/512+1/512

=130/512

=0.253