Question

a student hits a target with the probability of 0.2 how many times should she shoot the target to ensure at least a 50% chance of hitting the target​

Answer 1

On her fourth shot she will guarantee to have more than 50% chance of hitting the target.

Since the student hits with probability of 0.2, then she misses with probability (1-0.2)=0.8.

So, after shooting n times, she will miss miss all of the hits with probability $(0.8)^n$

If she wants to ensure at least 50% , she should shoot a number n such that $(0.8)^n=0.5$

This can be solved by logarithms using the fact that

$a^x=y \iff Log_a y=x$

Then we'll have $Log_{0.8} 0.5=x$

Using a calculator we can find that

$Log_{0.8} 0.5=3.10628372...$

That means on her third shot, she will be closer to 50% and on her fourth shot, She will have more than 50% chance of hitting the target.