Probability issue

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January 3rd 2011, 08:57 AM
Mathematicsfan

Probability issue

I have been trying desperately to solve this task, unfortunately I had no success whatsoever.
Here is the task:
"In a certain experience the probability of success is"P" (0<P<1).
It's known that if all four tests are executed then the probability of all of them to succeed is multiply 16 from the probability that all four experiences will fail. A: Find P."

final result is : 2\3

So I was able to calculate according to Bernoulli's table and get this equation ;
16P*(1-p)^4=1P^4*(1-p)^0
^=Power.
Can any one please help me solving this whole task please?
January 3rd 2011, 09:27 AM
Plato

You have set every thing up correctly.
Now it is just basic algebra.

Solve $p^4=16(1-p)^4$ .
Do the algebra.
January 3rd 2011, 09:43 AM
Mathematicsfan

I just don't know how to solve this equation, I forgot how to loose the Power ^4 and make it easy for solving.
Can you help me with the rest of the equation please?
January 3rd 2011, 09:52 AM
Plato

Here is a hint:
$16q^4-p^4=(4q^4-p^4)(4q^4+p^4)=(2q^2-p^2)(2q^2+p^2)(4q^4+p^4)$ .

Algebra is required to do this course material. Review your algebra.
January 3rd 2011, 10:02 AM
Mathematicsfan

I just can't seem to understand this method.
Is there any other way to decrease the Power ? ^4 ?
I need an example to follow according to and then I'll be able to understand all fluently.
Thank you very much.
January 3rd 2011, 10:34 AM
Plato

Quote:

Originally Posted by Mathematicsfan

I just can't seem to understand this method.
Is there any other way to decrease the Power ? ^4 ?
I need an example to follow according to and then I'll be able to understand all fluently.
Thank you very much.

Do you just want it done for you?
If so, maybe someone else will do it.
January 3rd 2011, 10:37 AM
Mathematicsfan

No I just need your help solving this.
I can't solve it.
I don't know what to do next with the equation.
Can't you help me decreasing the Power ? I want to solve it by my self but I'll need guidance.
January 3rd 2011, 11:06 AM
Mathematicsfan

Understood thanks a lot can be locked
January 3rd 2011, 02:01 PM
mr fantastic

Quote:

Originally Posted by Mathematicsfan

No I just need your help solving this.
I can't solve it.
I don't know what to do next with the equation.
Can't you help me decreasing the Power ? I want to solve it by my self but I'll need guidance.

Take the 4th root of both sides (suggested by the fact that everything is raised to the power of 4. Note: 16 = 2^4 ....) and note that p > 0.

The resulting equation is trivial to solve.