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A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 4? Select the correct answer from above options

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Correct Answer - 11 36 11 Clearly, n ( S ) = ( 6 × 6 ) = 36 n . Let E 1 E = event that the first throw shows a 4, and E 2 = E event that the second throw shows a 4. Then, ( E 1 ∩ E 2 ) = ( event that each throw shows a 4. ∴ E 1 = { ( 4 , 1 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) , ( 4 , 6 ) } , ∴ and E 2 = { ( 1 , 4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , 4 ) , ( 5 , 4 ) , ( 6 , 4 ) } E , ∴ ( E 1 ∩ E 2 ) = { ( 4 , 4 ) } . ∴ Now, use P ( E 1 ∪ E 2 ) = P ( E 1 ) + P ( E 2 ) − P ( E 1 ∩ E 2 ) . P

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