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 
.