For my own reference

[A-A-Abdelhamid]

ε1 = 0.2 ε2 = 0.25 ε3 = 0.3

P(at least two leptons)= {ε1 ε2 ε3} + {ε1ε2} + {ε1ε3} + {ε2*ε3}

= {0.2 0.25 0.3} + { 0.2 0.25} + {0.2 0.3} + {0.25 * 0.3} = 0.2

Using the formula manually and by code give the result as 0.155

1 - P [None passing] - [Only ONE only passing] = 1- [(1-ε1) (1-ε2) (1-ε3)] - [(ε1 (1-ε2) (1-ε3)) +(ε2 (1-ε1) (1-ε3)) +(ε3 (1-ε1) (1-ε2))] = 1- [(1-0.2)(1-0.25)(1-0.3)] - (0.2(1-0.25)(1-0.3)) - (0.25(1-0.2)(1-0.3)) - (0.3(1-0.2)(1-0.25))

= 0.155

the code gives the result as 0.15500000000000003

ε1 = 0.2 ε2 = 0.25 ε3 = 0.3 ε4 = 0.25

P(at least two leptons)= {ε1 ε2 ε3}+ {ε1 ε2 ε3ε4 } + {ε1ε2} + {ε1ε3} + {ε2ε3}