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Q8Section A (Section A)8 of 60

Probability that at least two events occur

Let E1,E2E_1, E_2 and E3E_3 be three events such that P(E1∩E2)=14,P(E1∩E3)=P(E2∩E3)=15andP(E1∩E2∩E3)=16.P(E_1\cap E_2)=\frac{1}{4},\quad P(E_1\cap E_3)=P(E_2\cap E_3)=\frac{1}{5}\quad\text{and}\quad P(E_1\cap E_2\cap E_3)=\frac{1}{6}. Then, among the events E1,E2E_1, E_2 and E3E_3, the probability that at least two events occur, equals

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