Statistics Homework help

Question

A poll is given, showing 65% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?

Answer 1

7C1(.65^1)(.35^6)

7!/6!1!)(.65)(.35^6)

=4.55(1.838265625x10^-3)

= 8.364108594 x 10^-3

=0.008364108594

= about 0.84% chance of exactly one favoring the new building project out of a random seven

less than 1% chance, almost 1%

that looks about right

chance of none favoring out of 7 is nearly zero %

chances of more than 1 is nearly 99%

chances of exactly r out of n with favorable odds x where 0<x<1 is

(nCr)(x^r)((1-x)^(n-r))= (n!/r!(n-r)!)(x^r)((1-x)^(n-r))

in this particular problem

n=7, r=1, x=.65, 1-x =.35

plug them in and simplify