Q. 225.0( 2 Votes )

# 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.

Answer :

Given that,

⇒ P(A_{P}) = P(A passing an examination)

⇒

⇒ P(A_{N}) = P(A Not passing an examination)

⇒

⇒

⇒ P(B_{P}) = P(B passing an examination)

⇒

⇒ P(B_{N}) = 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(S_{A}) = 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(S_{one}) = P(Only one of them passed the examination)

⇒ P(S_{one}) = 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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