# Math Help - unique probability question

1. ## 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

2. 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

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

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

and so on.

the probability of 10 or more preferring A or B is

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

since p=q=0.5

and $\binom{15}{k}=\binom{15}{15-k}$

3. This may be simplified to

$(2)(0.5)^{15}\left(\binom{15}{5}+\binom{15}{4}+\bi nom{15}{3}+\binom{15}{2}+\binom{15}{1}+1\right)$

as p=q=0.5