Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

A, B. C and D are mutually exclusive and exhaustive events. If 2...

A, B. C and D are mutually exclusive and exhaustive events. If 2P(A)=3P(B)=4P(C)=5P(D)2 \mathrm{P}(\mathrm{A})=3 \mathrm{P}(B)=4 \mathrm{P}(\mathrm{C})=5 \mathrm{P}(\mathrm{D}), then what is 77P(A)77 \mathrm{P}(\mathrm{A}) equal to?

Options

  1. A12
  2. B15
  3. C20
  4. D30

Correct answer

D. 30

Step-by-step solution

 Let 2P(A)=3P(B)=4P(C)=5P(D)=kNow P(A)+P(B)+P(C)+P(D)=1⇒k2+k3+k4+k5=1⇒30k+20k+15k+12k60=1⇒77k=60⇒k=6077P(A)=k2=3077⇒77P(A)=30\begin{aligned} & \text{ Let } 2 P(A)=3 P(B)=4 P(C)=5 P(D)=k \\ & \text{Now } P(A)+P(B)+P(C)+P(D)=1 \\ & \Rightarrow \frac{k}{2}+\frac{k}{3}+\frac{k}{4}+\frac{k}{5}=1 \\ & \Rightarrow \frac{30 \mathrm{k}+20 \mathrm{k}+15 \mathrm{k}+12 \mathrm{k}}{60}=1 \\ & \Rightarrow 77 \mathrm{k}=60 \Rightarrow \mathrm{k}=\frac{60}{77} \\ & P(A)=\frac{\mathrm{k}}{2}=\frac{30}{77} \\ & \Rightarrow 77 \mathrm{P}(\mathrm{A})=30\end{aligned}
Practice Probability on Quantrex Academy →

More from Probability

Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026Three events A , B and C are such that A and B are disjoint, A and C are independent, B… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026For a Binomial distribution with mean 6 and standard deviation 2 , what is the value of… NDA 2026Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3… NDA 2026In an entrance test there are multiple choice questions. There are four options for each… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Consider the following statements in respect of the events A , B , C : I. (A B C) ( A B C… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026The probability that a family owns a laptop is 0.68 ; that it also owns a desktop is 0.56… NDA 2025An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is… NDA 2025An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is… NDA 2025Under which of the following conditions may binomial distribution be used? I. The number… NDA 2025Three faces of a die are black, two faces are white and one face is red. The die is… NDA 2025A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6… NDA 2025 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs