Explanation
Calculation:
Let E be the event that a head appears.
Let C1,C2, and C3 be the events of selecting a fair coin, a two-headed coin, and a weighted coin, respectively.
Since one coin is selected at random from three:
Now, the probability of getting a head for each coin is:
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For a fair coin (C1): P(E∣C1)=21
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For a two-headed coin (C2): P(E∣C2)=1
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For a weighted coin (C3): P(E∣C3)=31
Using the Law of Total Probability:
P(E)=P(C1)⋅P(E∣C1)+P(C2)⋅P(E∣C2)+P(C3)⋅P(E∣C3)
P(E)=(31×21)+(31×1)+(31×31)
To solve, find a common denominator (18):
