# unique probability question

• Mar 6th 2010, 02:31 PM
alexandrabel90
unique probability question
A company had developed 2 brands of floor wax, brand A and B. both waxes are applied to the floor surfaces in each of 15 houses. assume that there is actually no difference in the quality of the two brands, what is the probability that ten or more homeowners would states a preference for either brand A or B?

THanks
• Mar 6th 2010, 03:30 PM
Quote:

Originally Posted by alexandrabel90
A company had developed 2 brands of floor wax, brand A and B. both waxes are applied to the floor surfaces in each of 15 houses. assume that there is actually no difference in the quality of the two brands, what is the probability that ten or more homeowners would states a preference for either brand A or B?

THanks

Hi alexandrabel90,

This is binomial,

if p is the probability A is preferred and q is the probability B is preferred, then

$\displaystyle p^{15}$ is the probability all prefer A

$\displaystyle \binom{15}{14}p^{14}q$ is the probability of 14 preferences for A

and so on.

the probability of 10 or more preferring A or B is

$\displaystyle 2\left(\binom{15}{5}p^{10}q^5+\binom{15}{4}p^{11}q ^4+\binom{15}{3}p^{12}q^3+\binom{15}{2}p^{13}q^2+\ binom{15}{1}p^{14}q+p^{15}\right)$

since p=q=0.5

and $\displaystyle \binom{15}{k}=\binom{15}{15-k}$
• Mar 7th 2010, 06:15 AM
$\displaystyle (2)(0.5)^{15}\left(\binom{15}{5}+\binom{15}{4}+\bi nom{15}{3}+\binom{15}{2}+\binom{15}{1}+1\right)$