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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

A problem is given to three students A, B and C , whose...

A problem is given to three students A,BA, B and CC, whose probabilities of solving the problem independently are 12,34\frac{1}{2}, \frac{3}{4} and pp respectively. If the probability that the problem can be solved is 2932\frac{29}{32}, then what is the value of pp ?

Options

  1. A25\frac{2}{5}
  2. B23\frac{2}{3}
  3. C13\frac{1}{3}
  4. D14\frac{1}{4}

Correct answer

D. 14\frac{1}{4}

Step-by-step solution

 Given P(A)=12,P(B)=34,P(C)=P⇒1−P(Aˉ)⋅P(Bˉ)P(Cˉ)=2932⇒1−12×14×(1−P)=2932⇒P=14\begin{aligned} & \text{ Given } \mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{3}{4}, \mathrm{P}(\mathrm{C})=\mathrm{P} \\ & \Rightarrow 1-\mathrm{P}(\bar{A}) \cdot \mathrm{P}(\bar{B}) \mathrm{P}(\bar{C})=\frac{29}{32} \\ & \Rightarrow 1-\frac{1}{2} \times \frac{1}{4} \times(1-\mathrm{P})=\frac{29}{32} \\ & \Rightarrow \mathrm{P}=\frac{1}{4}\end{aligned}
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