Question

A coin is tossed twice. Alice claims that the event of getting 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. Discuss whether she is right and if it makes a difference if the coin is fair or unfair.

Answer 1

Alice is not correct. The event of getting two heads is more 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.

Step-by-step explanation:

To determine if Alice is right, let's consider the two scenarios:

1. If we know that the first toss is a head, the possible outcomes for the second toss are only two: head or tail. So, the probability of getting two heads is 1/2.
2. If we know that at least one of the tosses is a head, there are three possible outcomes: HH, HT, and TH. So, the probability of getting two heads is 1/3.

Therefore, Alice is not correct. The event of getting two heads is more 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.

Whether the coin is fair or unfair does not make a difference in this case.