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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

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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. Select the correct answer from above options

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Correct Answer - (i) 0.054 (ii) 0.056 (iii) 0.348 (i) P(getting all A grades) =P(A1A2A3)=P(A1)×P(A2)×P(A3). (ii) P(getting no A grade) =P( ˉ A 1 ˉ A 2 ˉ A 3)=P( ˉ A 1)×P( ˉ A 2)×P( ˉ A 3). (iii) P(getting exactly two a grades) =P[( ˉ A 1A2A3)or(A1 ¯ A2 A3)or(A1A2 ˉ A 3)] =P( ˉ A 1A2A3)+P(A1 ˉ A 2A3)+P(A1A2 ˉ A 3) ={P( ˉ A 1)×P(A2)×P(A3)}+{P(A1)×P( ˉ A 2)×P(A3)}+{P(A1)×P(A2)×P( ˉ A 3)}.

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