A coin is tossed twice. Alice claims that the event of two

Chapter , Problem 15

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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?

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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 \(E_{2}\).

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