   SEARCH HOME Math Central Quandaries & Queries  Question from Amy, a student: 1-(1-P)^75=0.05 We have two responses for you

Hi Amy,

I assume you are to solve for P. I would use logarithms to solve this problem. I am going to use the natural logarithm (log base e), called ln on my calculator, but you can use the common logarithm (log base 10) if you wish. You should do the calculatios yourself so I'm going to illustrate with different numbers.

Solve for P where

1 - (1- P)65 = 0.01

so

(1- P)65 = 1 - 0.01 = 0.99

Taking the natural logarithm of both sides I get

65 ln(1 - P) = ln(0.99)
ln(1 - P) = ln(0.99)/65 = -0.00015462

Thus

1 - P = e-0.00015462 = 0.999845
(If you used the common log you would need to find 10log(1-P) rather than eln(1-P))

and hence

P = 1 - 0.999845 = 0.000155

I hope this helps,
Penny

Hi Amy.

First isolate the major problem:

(1-P)^75 = 0.95

Remember your rules of exponents: (x^y)^z = x^(yz).

So if z = 1/y, then yz = 1 so you can eliminate the exponent: [(1-P)^75]^(1/75) = 1-P

That means the next step is just to apply the reciprocal of the exponent to both sides:

[ (1-P)^75 ] ^ (1/75) = 0.95 ^ (1/75)

1 - P = 0.95 ^ (1/75)

Solve for P:

P = 1 - 0.95 ^ (1/75)

and turn to your calculator for the rest.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.