Question

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.

Answer 1

Correct Answer - (i) 0.054 (ii) 0.056 (iii) 0.348
(i) P(getting all A grades)
`=P(A_(1) A_(2) A_(3))=P(A_(1))xxP(A_(2))xxP(A_(3))`.
(ii) P(getting no A grade)
`=P(bar(A)_(1) bar(A)_(2) bar(A)_(3))=P(bar(A)_(1))xxP(bar(A)_(2))xxP(bar(A)_(3))`.
(iii) P(getting exactly two a grades)
`=P[(bar(A)_(1) A_(2) A_(3)) or (A_(1) bar(A_(2)) A_(3))or (A_(1) A_(2) bar(A)_(3))]`
`=P(bar(A)_(1) A_(2) A_(3))+P(A_(1)bar(A)_(2) A_(3))+P(A_(1)A_(2)bar(A)_(3))`
`={P(bar(A)_(1))xxP(A_(2))xxP(A_(3))}+{P(A_(1))xxP(bar(A)_(2))xxP(A_(3))}+{P(A_(1))xxP(A_(2))xxP(bar(A)_(3))}`.