Explanation
1. Define the Events:
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C1: Picking a double-headed coin (2 coins).
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C2: Picking a double-tailed coin (1 coin).
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C3: Picking a normal coin (2 coins).
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LH: The event that the lower face is a head.
2. Probabilities of picking the coins:
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P(C1)=52
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P(C2)=51
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P(C3)=52
3. Conditional Probabilities of the lower face being a head (LH):
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For a double-headed coin, both sides are heads. Therefore, the lower face is always a head:
P(LH∣C1)=1
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For a double-tailed coin, both sides are tails. Therefore, the lower face can never be a head:
P(LH∣C2)=0
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For a normal coin, there is one head and one tail. The probability that the lower face is a head is:
P(LH∣C3)=21
4. Total Probability Calculation:
Using the Law of Total Probability:
P(LH)=P(C1)⋅P(LH∣C1)+P(C2)⋅P(LH∣C2)+P(C3)⋅P(LH∣C3)
Substitute the values:
P(LH)=(52×1)+(51×0)+(52×21)
Final Answer:
The probability that the lower face is a head is (c) 53.
