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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Probability

NDA 2018 · Mathematics · Probability

Let A, B and C be three mutually exclusive and exhaustive events...

Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P(B)=1.5P(A)\mathrm{P}(\mathrm{B})=1.5 \mathrm{P}(\mathrm{A}) and P(C)=0.5P(B)\mathrm{P}(\mathrm{C})=0.5 \mathrm{P}(\mathrm{B}), then P(A0\mathrm{P}(\mathrm{A} 0 is equal to

Options

  1. A3/4
  2. B4/13
  3. C2/3
  4. D1/2

Correct answer

B. 4/13

Step-by-step solution

As A, B and C are mutually exclusive and exhaustiveevent.exhaustive event.∴P(A)+P(B)+P(C)=1⇒P(A)+32P(A)+12×32P(A)=1⇒134P(A)=1⇒P(A)=413\begin{aligned} & \therefore \quad \mathrm{P}(\mathrm{ A})+\mathrm{P}(\mathrm{ B})+\mathrm{P}(\mathrm{C})=1 \\ & \Rightarrow \quad \mathrm{P}(\mathrm{ A})+\frac{3}{2} \mathrm{P}(\mathrm{ A})+\frac{1}{2} \times \frac{3}{2} \mathrm{P}(\mathrm{ A})=1 \\ & \Rightarrow \quad \frac{13}{4} \mathrm{P}(\mathrm{ A})=1 \\ & \Rightarrow \quad \mathrm{P}(\mathrm{ A})=\frac{4}{13} \end{aligned}$$
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