ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. find the probability that there is at least one defective egg.

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Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

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Updated on : 2022-09-05

Probability of defective eggs =10%

Solution Verified by Toppr p= 100 10 ​ = 10 1 ​

(Probability of good eggs)=q

q=1−p=1− 100 10 ​ = 10 9 ​

(Probability of at least one egg defective out of 10)

p(1)+p(2)+p(3)+...

=p(0)+p(1)+p(2)+...+p(10)−p(0)

=[p(0)+p(1)+p(2)+...+p(10)]−p(0)

=1−p(0)=1−( 10 9 ​ ) 10

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Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

Probability of an egg being defective = 10/100 = 1/10 So, probability of an egg being non-defective = 1-0.1=0.9 10 eggs are drawn successively with replacement. So, the probability of getting no defective egg = (0.9)^10 Hence, the probability that there is at least one defective egg = 1-(0.9)^10.

Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

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Text Solution Solution

Probability of an egg being defective

= 10 100 = 1 10

So, probability of an egg being non-defective

= 1 − 0.1 = 0.9 10

eggs are drawn successively with replacement.

So, the probability of getting no defective egg

= ( 0.9 ) 10

Hence, the probability that there is at least one defective egg =

1 − ( 0.9 ) 10 . Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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Ten Eggs Are Drawn Successively, with Replacement, from a Lot Containing 10% Defective Eggs. Find the Probability that There is at Least One Defective Egg.

Ten Eggs Are Drawn Successively, with Replacement, from a Lot Containing 10% Defective Eggs. Find the Probability that There is at Least One Defective Egg.

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Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

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SOLUTION

Let X be the number of defective eggs drawn from 10 eggs.

Then, X follows a binomial distribution with

n=10

Let p be the probability that a drawn egg is defective.

∴p=10 % = 110,q=910

Hence, the distribution is given by

Hence, the distribution is given by

P(X=r)=10Cr(110)r(910)10−r,r=0,1,2....10

there is at least one defective egg

P( there is at least one defective egg )=P(X≥1)

=1−P(X=0)

=1−10C0(110)0(910)10−0

=1−(910)10 =1−9101010

Concept: Bernoulli Trials and Binomial Distribution

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Chapter 33: Binomial Distribution - Exercise 33.1 [Page 14]

Q 40 Q 39.3 Q 41

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RD Sharma Class 12 Maths

Chapter 33 Binomial Distribution

Exercise 33.1 | Q 40 | Page 14

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