calculate size of sample to reach wanted probability 
You are recording neural activity in a cortical brain region. This
brain region is known to contain excitatory and inhibitory neurons
randomly distributed in space. In the cortex, the number of excitatory
neurons is 4 times than the inhibitory neurons. You record blindly the
neural activity, that is, you don’t know the type of the recorded
neurons.  Note that each time you stick your electrode you might
record the same neuron

*

*Your recorded 100 neurons. How many neurons you expect to see from each type?

*How many neurons must you record so that you will have at least one neuron from each type with probability of >0.95? (use matlab to
estimate the number, it is not easy to solve the equation
analytically)



*

*I think that the answer for this is 80/20, am I right? (seems to easy to be true)

*I'm not sure how to start with this. am I suppose to calculate the CDF? I was thinking that if the   probability of hitting inhibitory neuron is the smallest(0.2?) than I should just calculate the value of X for CDF(X) =0.95. is this the correct way to solve this?


For (1): spot on.
A hint for (2): note that
$$
\begin{align*}
P(\text{at least one of each})&=1-P(\text{all excitatory or all inhibitory})\\
&=1-(P(\text{all excitatory})+P(\text{all inhibitory})\\
&=1-P(\text{all excitatory})-P(\text{all inhibitory}).
\end{align*}
$$
If you take $n$ measurements, can you compute the probability that they were all excitatory?  The probability they were all inhibitory?
