Consider an experiment of a single throw of a pair of unbiased normal dice. Let three events ε 1 , ε 2 and ε 3 are defined as follows ε 1 : getting prime numbered face on each dice ε 2 : getting the same number on each dice ε 3 : getting th

Question

Consider an experiment of a single throw of a pair of unbiased normal dice. Let three events ε 1 , ε 2 and ε 3 are defined as follows ε 1 : getting prime numbered face on each dice ε 2 : getting the same number on each dice ε 3 : getting the sum of 4 on two dice Which of the following is not true?

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Correct answer: C. P ε 3 ε 1 = 2 9

ε 1 = 2,2 2,3 2,5 , 3,2 , 3,3 , 3,5 , 5,2 , 5,3 , 5,5 ε 2 = 1,1 2,2 3,3 , 4,4 , 5,5 , 6,6 ε 3 = 1,3 , 3,1 , 2,2 P ε 1 = 9 36 = 1 4 , P ε 2 = 6 36 = 1 6 , P ε 3 = 3 36 = 1 12 P ε 1 , P ε 2 , P ε 3 are in A.P. P ε 1 ∩ ε 2 = 3 36 ≠ P ε 1 ⋅ P ε 2 D e p e n d e n t P ε 3 ε 1 = P ε 3 ∩ ε 1 P ε 1 = 1 36 9 36 = 1 9

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