Maths · Probability: Probability of an event, addition and multiplication theorems of probability
A coin is tossed three times, where (i) head on third toss, heads on first two t
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 \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)
- A. 0.42,0.50,0.85
- B. 0.50,0.42,0.85
- C. 0.85,0.42,0.30
- D. .0.42, 0.46, 0.47
Step-by-step solution
For (i): P(E|F) = P(E∩F)/P(F) = (1/8)/(2/8)=1/2=0.50. For (ii): E = at least 2 heads (4 outcomes), F = at most 2 heads (7 outcomes), E∩F = 3 outcomes, so P(E|F)=3/7≈0.42. For (iii): E = at most 2 tails (7 outcomes), F = at least 1 tail (7 outcomes), E∩F = 6 outcomes, so P(E|F)=6/7≈0.85. Thus the correct sequence is 0.50,0.42,0.85.
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