Multiple choice

A coin is tossed three times, where (i) $E$ : head on third toss, $F$ : heads on first two tosses (ii) $E$ : at least tow heads, $F$ : at most two heads (iii) $E$ : at most two tails, $F$ : at least one tail Determine $ P\left( E|F \right) $

  1. $0.42,0.50,0.85$
  2. $0.50,0.42,0.85$
  3. $0.85,0.42,0.30$
  4. $.0.42,0.46,0.47$
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B Correct answer
AI explanation

For part (i), E contains 4 outcomes (HHH, HHT, THH, TTH) and F contains 2 outcomes (HHH, HHT), so P(E given F) is 2/4 = 0.50. For part (ii), E (at least two heads) has 4 outcomes and F (at most two heads) has 7 outcomes, with their intersection holding 3 outcomes (HHT, HTH, THH), making the probability 3/7 = 0.42. For part (iii), E (at most two tails) has 7 outcomes and F (at least one tail) has 7 outcomes, with their intersection containing 6 outcomes, making the probability 6/7 = 0.85. The final values are 0.50, 0.42, 0.85.

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