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.

Explanation

It is Given that ,

`since` P (Neelam gets A grade in Physics) =0.2

`since` P( Neelam gets A grade in chemistry )=0.3

`since` P( Neelam gets A grade in Mathematics )=0.9

`Rightarrow` P (Neelam gets exactly two A grades)
`=P(bar{A} cap B cap C)+P(A cap bar{B} cap C)+P(A cap B cap bar{C})`

`=P(bar{A}) cdot P(B) cdot P(C)+P(A) cdot P(bar{B}) cdot P(C)+P(A) P(B) P(bar{C})`

`=(1-0.2) 0.3 times 0.9+0.2(1-0.3) times 0.9+
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