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SEAMO 2027 - Paper F - SET 05 - Self-study Question 12

SEAMO · SEAMO 2027 - Paper F - SET 05 - Self-study

Question 12

A student sits tests I, II and III. The student is successful if he passes either tests I and II or tests I and III. The passing probabilities are $p,q,1/2$, respectively. If his probability of success is $1/2$, which of the following can be $p,q$?

Conditional self-study version: assume the three passing events are mutually independent. The source does not state independence; without it, more than one listed pair can be possible. Choose under this explicit assumption.
  1. $p=q=1$
  2. $p=q=1/2$
  3. $p=1,\ q=1/2$
  4. $p=1,\ q=0$
  5. $p=1/2,\ q=0$