Binomial Distribution Question?

Question

A scientific experiment is carried out a number of times in the hope that a later analysis of the data finds at least one success. Let n be the number of times that the experiment is conducted and suppose that the probability of success is p = 0.2 Assuming that the experiments are conducted independently from one another, what is the number of experiments that must be conducted to be 95% sure of having at least one success?

Unsure of how to do this. All I know is that it has to do with binomial distribution.

Answer 1

Hint:

If the experiment is carried out $n $ times, $$\text {Pr (at least one success)}$$ $$ = 1 - \text {Pr (No success)}$$ $$ = 1- (0.8)^n \geq 0.95$$

Hope you can take it from here.

Answer 2

Back to basics.

The probability for having no success in any particular trial will be $(1-p)$.

Since the trials are independent, the probability for having no success among $n$ of them will be a $(1-p)^n.$

Therefore the probability for having at least one success among $n$ trials will be: $1-{{(1-p)^n}}$ through the rule of complementary probability.

Substitute $p=0.2$ and find the value for $n$ which makes $(1-{{0.8^n}})\geqslant 0.95$, using algebraic manipulation.

That is all.