Please tell me the way that we use Binomial Distribution for this. Each of six r
ID: 3206675 • Letter: P
Question
Please tell me the way that we use Binomial Distribution for this.
Each of six randomly selected cola drinkers is given a glass containing cola S and one containing cola F. The glasses are identical in appearance except for a code on the bottom to identify the cola. Suppose there is actually no tendency among cola drinkers to prefer one cola to the other. That is, let theta = 0.5 be the probability that a selected individual prefers S. Find the probability that exactly three drinkers prefer cola S. at least three drinkers prefer cola S, at most one drinker prefers S.Explanation / Answer
N=6
n=3
p=.5
q=1-p=.5
a) Exactly 3
p(x=3) = c(N,n) * p^n * q^(N-n) = c(6,3) * .5^3 * .5^3
= 0.3125
b) At least :
p(x>=3) = 1 - p(x<3) = 1 - 0.34375
= 0.6563
c) At most:
N=6
n=1
p(x<=1) = c(6,0) * .5^0 * .5^6 + c(6,1) * .5^1 * .5^5
= 0.1094