Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

There are 3 coins in a box. One is a two-headed coin; a fair coin...

There are 3 coins in a box. One is a two-headed coin; a fair coin another is; and third is biased coin that comes up heads 75%75 \% of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Options

  1. A29\frac{2}{9}
  2. B13\frac{1}{3}
  3. C49\frac{4}{9}
  4. D59\frac{5}{9}

Correct answer

C. 49\frac{4}{9}

Step-by-step solution

P(T)=13;P(HT)=1P(F)=13,P(HF)=12P(B)=13,P(HB)=34P(TH)=P(T)⋅P(HT)P(T)⋅P(HT)+P(F)⋅P(HF)+P(B)⋅P(HB)⇒P(TH)=1313+16+14=194=49\begin{aligned} & P(T)=\frac{1}{3} ; P\left(\frac{H}{T}\right)=1 \\ & P(F)=\frac{1}{3}, P\left(\frac{H}{F}\right)=\frac{1}{2} \\ & P(B)=\frac{1}{3}, P\left(\frac{H}{B}\right)=\frac{3}{4} \\ & P\left(\frac{T}{H}\right)=\frac{P(T) \cdot P\left(\frac{H}{T}\right)}{P(T) \cdot P\left(\frac{H}{T}\right)+P(F) \cdot P\left(\frac{H}{F}\right)+P(B) \cdot P\left(\frac{H}{B}\right)} \\ & \Rightarrow P\left(\frac{T}{H}\right)=\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{6}+\frac{1}{4}} \\ & =\frac{1}{\frac{9}{4}}=\frac{4}{9}\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