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Hello, I have a small confusion on the followings: Question B (i) shouldn't "P(c)" be 1/2...

Hello, I have a small confusion on the followings: Question B (i) shouldn't "P(c)" be 1/2 instead of 1/12? Thanks in advance

Question 1

You will receive a prize if both a fair coin lands "heads" AND a fair die lands "6". After the coin is flipped and the die is rolled you ask if AT LEAST ONE of these events has occurred and you are told "yes."

B i) Specify the joint distribution, ?(?) in terms of its constituent conditional distributions

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Answer #1

P(getting head)=P(A)=1/2

P(getting 6 on die)=P(B)=1/6

These two events are independent.

When two events are independent: P(A B)=P(A)*P(B)

P(c)=P(A B))=1/2*1/6=1/12

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