Q. 405.0( 3 Votes )

Ten eggs are draw

Answer :

Given that, 10 eggs are drawn successively.


Defective eggs in the lot = 10%


Let p be the probability that the eggs drawn from the lot are defective.


p = 10%




Then, q is the probability that the eggs drawn from the lot is not defective.


And, p + q = 1


q = 1 – p





Let X be a random variable that represents defective eggs picked out of n eggs from the lot.


Then, the probability of taking r defective eggs out of n eggs from the lot is given by,


P (X = r) = nCrprqn-r


Here, n = 10


Putting the values of n, p, and q in the above formula, we get


…(i)


We need to find the probability of getting at least one defective egg from the lot.


This is represented as,


Probability = P (X ≥ 1)


This is also written as,


P (X ≥ 1) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7) + P (X = 8) + P (X = 9) + P (X = 10)


Or


P (X ≥ 1) = 1 – P (X < 1)


P (X ≥ 1) = 1 – P (X = 0)


Putting r = 0 in P (X = r) formula in (i), we get





, the probability of getting at least one defective egg from the lot is .


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