# The probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events: ‘A passes’, ‘B passes’ as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.

Given that,

P(AP) = P(A passing an examination)

P(AN) = P(A Not passing an examination)

P(BP) = P(B passing an examination)

P(BN) = P(B Not passing an examination)

We need to find probability that:

i. Only A passing the examination

ii. Only one of them passing the examination

P(SA) = P(Only A passing the examination)

This happens only in the case B must fail

Since passing examination is an independent event their probabilities multiply each other

P(Sone) = P(Only one of them passed the examination)

P(Sone) = P(only A passed the examination) + P(only B passed the examination)

Since passing examination is an independent event their probabilities multiply each other

The required probabilities are .

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