Using GDC to solve problems

GDC Method:

1. The GDC has a function called "Inverse Binomial \(N\)" where it returns the answer for total number of trials \(n\), when the following are given:
   1. Probability of success: \(p\)
   2. Cumulative probability \(\mathrm{P}(X \leq x)\)

In order to rewrite into the format that GDC can solve, we start out with

\[\mathrm{P}(X \geq 1) > 0.95\]

And rewrite into

\[\mathrm{P}(X \leq 0) \leq 0.05\]

*Note that the upper limit must be inclusive in the cumulative probability.

2. Open a new 'Calculator' page and go to: menu > 6: Statistics > 5: Distribution > D: Inverse Binomial N...

3. Fill in the cumulative probability which is the maximum value of probability allowed, and probability of success p.
   The successes x is the upper limit of x for the cumulative probability.
   You may want to click Matrix form, where they show you the two values of n before and after surpassing \(0.05\) the required value.

4. As shown in the result, when \(n = 8\), \(P(X \leq 0) = 0.0577\) and when \(n = 9\), \P(X \leq 0) = 0.0404\), and so \(n =9\) is the solution.