Mathematics · Probability

JEE Advanced 2020 — Paper 2 — Question 35

The probability that a missile hits a target successfully is 0.75 . In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95 , is $\_\_\_\_$

Answer: 6

Numerical answer — enter this value.

Step-by-step solution

Let ' $n$ ' be the number of missiles fired

$\Rightarrow$ probability of atleast 3 successful hits

\begin{aligned} & =1-{ }^{n} C_{0}\left(\frac{1}{4}\right)^{n}-{ }^{n} C_{1}\left(\frac{3}{4}\right)\left(\frac{1}{4}\right)^{n-1}-{ }^{n} C_{2}\left(\frac{3}{4}\right)^{2}\left(\frac{1}{4}\right)^{n-2} \\& \Rightarrow 1-{ }^{n} C_{0}\left(\frac{1}{4}\right)^{n}-{ }^{n} C_{1}\left(\frac{3}{4}\right)\left(\frac{1}{4}\right)^{n-1}-{ }^{n} C_{2}\left(\frac{3}{4}\right)^{2}\left(\frac{1}{4}\right)^{n-2} \geq 0.95 \\& \Rightarrow 9 n^{2}-3 n+2 \leq \frac{4^{n}}{10} \\&\end{aligned}

$\Rightarrow$ minimum value of $n$ is $6(n \in N)$

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Exam: JEE Advanced 2020
Paper: Paper 2
Subject: Mathematics
Chapter: Probability
Topic: Random Variables, Binomial & Poission Distribution

Two fair dice, each with faces numbered 1,2,3,4,5 and 6 , are rolled together and the sum of the numbers on the faces is observed. This…

Answer: 6

Step-by-step solution

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