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  • Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 16

Need solution for RD sharma maths class 12 chapter 30 probablity exercise Very short answer question, question 16

Answers (1)

best_answer

The required probability is 3p^{2}-3p^{3}

Hint:

Use the relation ,

P(atleast two of A,B,C occurs) =  P(A\cap B\cap C')+P(A\cap B' \cap C)+P(A'\cap B \cap C)

Given:

A, B & C are three independent events such that P(A)=P(B)=P(C)=p

Explanation:

We have, P(A)=P(B)=P(C)=p

\Rightarrow P(A')=P(B')=P(C')=1-p

Now,

P(atleast two of A,B,C occurs) =  P(A\cap B\cap C')+P(A\cap B' \cap C)+P(A'\cap B \cap C)

= P(A).P(B).P(C')+P(A).P(B').P(C) +P(A').P(B).P(C)

   ( \thereforeA , B & C are independent )
=p.p(1-p)+p(1-p).p+(p-1)p.p\\ =p^{2}(1-p)+p^{2}(1-p)+p^{2}(1-p)\\ =(1-p) 3p^{2}\\ = 3p^{2}- 3p^{3}

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