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A coin is tossed twice. Alice claims that the event of two
Chapter , Problem 15(choose chapter or problem)
A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is a head. Is she right? Does it make a difference if the coin is fair or unfair? How can we generalize Alice's reasoning?
Questions & Answers
QUESTION:
A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is a head. Is she right? Does it make a difference if the coin is fair or unfair? How can we generalize Alice's reasoning?
ANSWER:Step 1 of 2
Given that,
A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is a head.
Let:
The probability of head when the coin is tossed be p.
The event that the first toss is a head be \(E_{1}\).
The event that the second toss is a head be \(E_{2}\).