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Neelam has offered physics, chemistry and mathematics in Class XII. She estimates that her probabilities of receiving a grade A in these courses are 0.2, 0.3 and 0.9 respectively. Find the probabilities that Neelam receives 

(i) all A grades 

(ii) no A grade 

(iii) exactly 2 A grades.

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Given : let A , B and C represent the subjects physics,chemistry and mathematics respectively ,

the probability of neelam getting A grade in these three subjects is given i.e , 

P(A) = 0.2 , P(B) = 0.3 and P(C) = 0.9

\(\Rightarrow\) P(\(\overline A\)) = 0.8 , P(\(\overline B\)) = 0.7 and P(\(\overline C\)) = 0.1

To Find: 

(i) The probability that neelam gets all A grades

Here, P(getting all A grades) = P(A ∩ B ∩ C)

= P(A) x P(B) x P(C)

= 0.2 x 0.3 x 0.9

Therefore, The probability that neelam gets all A grades is 0.054.

(ii) no A grade

Here , P(getting no A grade) = P(\(\overline A\cap \overline B \,\cap \overline C\))

Therefore, The probability that neelam gets no A grade is 0.056.

(iii) excatly 2 a grades

P(getting excatly 2 A grades) 

= P(A and B and not c) + P (B and C and not A) + P (C and A and not B)

Therefore, The probability that neelam gets excatly 2 A grades is 0.348.

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