Question: A fair coin: P(H)=P(T)=0.5 . A two-headed coin: P(H)=1 . A coin is chosen at random from the box, i.e. either coin is chosen with

A fair coin: P(H)=P(T)=0.5 .

A two-headed coin: P(H)=1 .

A coin is chosen at random from the box, i.e. either coin is chosen with probability 1/2 , and tossed twice. Conditioned on the identity of the coin, the two tosses are independent.

Define the following events:

Event A : first coin toss is H .

Event B : second coin toss is H .

Event C : two coin tosses result in HH .

Event D : the fair coin is chosen.

are these event independent?

Event A: first coin toss is H. Event B: second coin toss is H. Event C: two coin tosses result in HH. Event D: the fair coin is chosen

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