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.

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

= 0.054

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

= 0.056

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

= 0.348

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