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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Probability

NDA 2022 · Mathematics · Probability

During war one ship out of 5 was sunk on an average in making a...

During war one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive safely?

Options

  1. A16625\frac{16}{625}
  2. B32625\frac{32}{625}
  3. C64625\frac{64}{625}
  4. D128625\frac{128}{625}

Correct answer

D. 128625\frac{128}{625}

Step-by-step solution

n=5,q=P( sunk )=15,P=1−15=45P(x=3)=5C3(45)3(15)2=128625\begin{aligned} & n=5, q=P(\text{ sunk })=\frac{1}{5}, P=1-\frac{1}{5}=\frac{4}{5} \\ & P(x=3)={ }^5 C_3\left(\frac{4}{5}\right)^3\left(\frac{1}{5}\right)^2=\frac{128}{625}\end{aligned}
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