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.

Question

Philoid · Accepted 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 .