Answer:
The probability that more than a third of the buyers would prefer brown is 0.8491.
Step-by-step explanation:
This is binomial problem with n=15 and p=0.50.
The binomial formula of probaility is:
P(X=x)=
More than a third of the buyers: 15÷3=5
We have to find P(x>5).
P(x>5) = 1 - P(x≤5) = 1 - P(x=0) - P(x=1) - P(x=2) - P(x=3) - P(x=4) - P(x=5)
P(x=0)==0.00003
P(x=1)==0.00046
P(x=2)==0.00320
P(x=3)==0.01389
P(x=4)==0.04165
P(x=5)==0.09164
P(x>5) = 1 - P(x≤5)= 1- 0.00003 - 0.00046 - 0.00320 - 0.01389 - 0.04165 - 0.09164 = 0.8491