Two fair dice are tossed. Let A be the event | vedclass

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(D) When two fair dice are tossed,the outcome of the first die does not affect the outcome of the second die.Event $A$ is that the first die shows an

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Independent

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(D) When two fair dice are tossed,the outcome of the first die does not affect the outcome of the second die.Event $A$ is that the first die shows an even number: $A = \{2, 4, 6\}$. The probability $P(A) = 3/6 = 1/2$.Event $B$ is that the second die shows an odd number: $B = \{1, 3, 5\}$. The probability $P(B) = 3/6 = 1/2$.The intersection $A \cap B$ represents the event where the first die is even $AND$ the second die is odd. The number of such outcomes is $3 	imes 3 = 9$ out of $36$ total outcomes.Thus,$P(A \cap B) = 9/36 = 1/4$.Since $P(A) 	imes P(B) = (1/2) 	imes (1/2) = 1/4$,we have $P(A \cap B) = P(A) 	imes P(B)$.Therefore,the events $A$ and $B$ are independent.

Two fair dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two events $A$ and $B$ are

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