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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots...

A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?

Options

  1. A18\frac{1}{8}
  2. B16\frac{1}{6}
  3. C14\frac{1}{4}
  4. D13\frac{1}{3}

Correct answer

A. 18\frac{1}{8}

Step-by-step solution

Here A,B\mathrm{A}, \mathrm{B} and C are independent events P(A)=56,P(B)=45,P(C)=34 and P(B‾)=1−P(B)=1−45=15∴P(A∩B‾∩C)=P(A)⋅P(B‾)⋅P(C)=56×15×34=18\begin{aligned} & \mathrm{P}(\mathrm{ A})=\frac{5}{6}, \mathrm{P}(\mathrm{ B})=\frac{4}{5}, \mathrm{P}(\mathrm{C})=\frac{3}{4} \\ & \text{ and } \mathrm{P}(\overline{\mathrm{ B}})=1-\mathrm{P}(\mathrm{ B})=1-\frac{4}{5}=\frac{1}{5} \\ & \therefore \mathrm{P}(\mathrm{ A} \cap \overline{\mathrm{ B}} \cap \mathrm{C})=\mathrm{P}(\mathrm{ A}) \cdot \mathrm{P}(\overline{\mathrm{ B}}) \cdot \mathrm{P}(\mathrm{C})=\frac{5}{6} \times \frac{1}{5} \times \frac{3}{4}=\frac{1}{8} \end{aligned}
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