Can you tell me what is the simplify of this calculation?

Question

Can you tell me what is the simplify of :

1-(1-P)^75 = 0.05

P = 0.000684

How did we get P = 0.000684?

Answer 1

Work with logarithms.

1 - (1 - p)⁷⁵ = 0.05

(1 - p)⁷⁵ = 0.95

75 log(1 - p) = log0.95

log(1 - p) = (log0.95) / 75

log(1 - p) = -2.9702 x 10^-4

Take 10^{( )} of both sides.

1 - p = 10^(-2.9702 x 10^-4) = 0.99932

p = 6.8368 x 10^-4 = 0.00068368 ≅ 0.000684