Multiple choice

Two coins are tossed once, where (i) $E$ : tail appears on one coin, $F$ : one coin shows head (ii) $E$ : no tail appears, $F$ : no head appears Determine $P\left( E|F \right) $

  1. $1,0$
  2. $1,0.2$
  3. $0,2$
  4. $1,3$
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A Correct answer
Explanation

For (i), the sample space is {HH, HT, TH, TT}. E={HT, TH}, F={HT, TH}, so P(E|F)=1. For (ii), E={HH}, F={TT}, so they are disjoint, P(E|F)=0.

AI explanation

For the first case, event F means one coin shows head, which guarantees the other coin is a tail, making P(E|F) = 1. For the second case, event F is no head appears, meaning both are tails, which makes it impossible to have no tail appear, so P(E|F) = 0. The required probabilities are 1 and 0.

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