# What is the probability when i attempt twice?

// I have never got probabilities' lessons , I only know some basics

Let's say the probability of me hitting the target ( let's consider hitting a bottle with a soccer ball ) in ONE ATTEMPT is calculated and it equals 0.3 .

Logically , when i try more than once i'm having a bigger chance of hitting it .

Then what will the probability of me hitting the target - at least once - if i try 15 times be ?

• You mean hitting at least once? Jul 5, 2014 at 6:25
• Yes definitely . Jul 5, 2014 at 6:30

Let us assume independence. The probably of missing on any attempt is $0.7$. So the probability of missing twice in a row is $(0.7)^2=0.49$. Thus the probability of hitting the bottle at least once in $2$ trials is $1-0.49$, that is, $0.51$. As your intuition told you, this is substantially larger than $0.3$.
The probability of missing $15$ times in a row is $(0.7)^{15}$, so the probability of hitting at least once is $1-(0.7)^{15}$. This is about $0.995$.
The probability that you will hit the target always remains $0.3$ each time you try. This is because each attempt is independent and is unaffected by successes and failures from previous attempts. The total probability of hitting the target all of the $15$ times you try will be
$P=(0.3)^{15}= 0.000000014348907$