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
P() = 0.8 , P() = 0.7 and P()= 0.1
To Find: i)The probability that neelam gets all A grades
Here, P(getting all A grades) = P( B C)
= P(A) P(B) P(C)
=0.2 0.3 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( )
= P( ) P( ) P( )
= 0.8 0.7 0.1
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)
= P( A B ) + P(B C ) + P(C A )
= P(A) P(B) P() + P(B) P(C) P() + P(C) P(A) P()
= [0.2 0.3 0.1] + [0.3 0.9 0.8] + [ 0.9 0.2 0.7]
= 0.006 + 0.216 +0.126
Therefore, The probability that neelam gets excatly 2 A grades is 0.348.
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