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// 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 ?

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  • $\begingroup$ You mean hitting at least once? $\endgroup$ Jul 5, 2014 at 6:25
  • $\begingroup$ Yes definitely . $\endgroup$
    – reaffer
    Jul 5, 2014 at 6:30

2 Answers 2

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We have to make some assumptions. The technically easiest assumption is that the events "hit the bottle" on the various trials are independent. This is not necessarily realistic. Maybe one gets rattled if one misses a few times. Or maybe one learns to correct one's aim.

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 $0.995$.

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  • $\begingroup$ Thanks , this is what i wanted to know and how i want to think in the future ! $\endgroup$
    – reaffer
    Jul 5, 2014 at 6:37
  • $\begingroup$ You are welcome. $\endgroup$ Jul 5, 2014 at 6:37
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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

$P=(0.3)^{15}= 0.000000014348907$

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