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Model Paper 6 — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsModel Paper 65 Marks
Question
The probability that Rohit will hit a shooting target is $\frac{2}{3}$. While preparing for an international shooting competition. Rohit aims to achieve the probability of hitting the target atleast once to be 0.99 . What is the minimum number of chances must he shoot to attain this probability?
✓

Answer

Given probability of hitting a shooting target $=p=\frac{2}{3}$.
So, $q =1- p =1-\frac{2}{3}=\frac{1}{3}$.
Let the number of trials be $n$.
The probability of hitting target atleast once $= P ( X \geq 1)=1- P (0)$
$
=1-{ }^n C_0 q^n=1-\left(\frac{1}{3}\right)^n
$
According to given,
$
\begin{array}{l}
1-\left(\frac{1}{3}\right)^n>0.99 \Rightarrow 1-\frac{1}{3^n}>\frac{99}{100} \\
\Rightarrow 1-\frac{99}{100}>\frac{1}{3^n} \Rightarrow \frac{1}{100}>\frac{1}{3^n} \\
\Rightarrow 100<3^n
\end{array}
$
$\Rightarrow 3^n>100$, which is satisfied if n is atleast 5.
Hence, Rohit must shoot the target at 5 times.

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