# Minimum value Probability Question

1. Sep 26, 2008

### l46kok

1. The problem statement, all variables and given/known data
When a conventional apging system transmits a message, the probability that the message will be received by the pager it is sent to is p. To be confident that a message is received at least once, a system transmits the message n times.

Assuming p = 0.8, what is the minimum value of n that produces a probability of 0.95 of receiving the message at least once?

3. The attempt at a solution
Ok, so the probability of message being transmitted per attempt is

First Attempt : 0.8
Second Attempt : 0.8(1-0.8)
Third Attempt : 0.8(1-0.8)^2

and so on.

So we could set up an equation

$$0.8 + \sum_{j=1}^\n \nnnnnnnnnnnnnnnn0.8(1-0.8)^j = 0.95$$

$$0.8 * \sum_{j=1}^\n \((1-0.8)^j = 0.15$$

$$\sum_{j=1}^\n \((1-0.8)^j = 0.1875$$

And I'm stuck here. There is no possible value for n for this summation to be satisfied (n needs to be an integer equal or greater than 1). Can anybody help?

Last edited: Sep 26, 2008
2. Sep 26, 2008

### l46kok

Ok, it's situation like these latex seriously does a commendable job of pissing me off. How would you write the summation of index starting from j = 1 until n?

3. Sep 26, 2008

### Dick

The probability the message is received on the first try is 0.8. The probability the messages is received on the second try given that the first one failed is (as you say) 0.8*(1-0.8)=0.16. The sum of the two is 0.96. Aren't you done?

4. Sep 26, 2008

### Dick

The same way you did in your last latex block. \sum_{j=1}^n whatever. $$\sum_{j=1}^n a_j$$.

Last edited: Sep 26, 2008