SOLUTION: Farmer Ze'ev has four chickens-two that lay white eggs and two that lay brown eggs. If each hen has a 0.6 probability of laying an egg on any given day: a) What is the average num

Question 909205: Farmer Ze'ev has four chickens-two that lay white eggs and two that lay brown eggs. If each hen has a 0.6 probability of laying an egg on any given day:
a) What is the average number of eggs he collects each day?
b) What is the probability of getting no eggs at all?
c) What is the probability of getting only brown eggs (i.e, one or two, but not none)?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
X~Binomial(n=6, p=0.6)
a)
Average = Mean = np = 6*0.6 = 3.6 eggs per day.

b) P[X=0] = (6 choose 0)*(0.6)^0(0.4)^6 = .0041
c) X~Binomial(n=4, p=0.6) Y~Binomial(n=2, p=0.6)
P[X=0, Y=1] + P[X=0,Y=2]
P[X=0] * (P[Y=1] + P[Y=2])

(0.4)^4 * [(2 choose 1)(.6)^1*(.4)^1 + (2 choose 2)(.6)^0(.4)^2] = .0164

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