Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

A coin is tossed twice. If E and F denote occurrence of head on...

A coin is tossed twice. If EE and FF denote occurrence of head on first toss and second toss respectively, then what is P(E∪F)P(E \cup F) equal to?

Options

  1. A14\frac{1}{4}
  2. B12\frac{1}{2}
  3. C34\frac{3}{4}
  4. D13\frac{1}{3}

Correct answer

C. 34\frac{3}{4}

Step-by-step solution

P(E)=12,P(F)=12P(E∪F)=P(E)+P(F)−P(E∩F)\begin{aligned}& P(E)=\frac{1}{2}, P(F)=\frac{1}{2} \\ & P(E \cup F)=P(E)+P(F)-P(E \cap F)\end{aligned} As E \ \text{ and } F are two independent event ∴P(E∩F)=P(E)⋅P(F)P(E∪F)=12+12−12⋅12=34\begin{aligned}& \therefore P(E \cap F)=P(E) \cdot P(F) \\ & P(E \cup F)=\frac{1}{2}+\frac{1}{2}-\frac{1}{2} \cdot \frac{1}{2}=\frac{3}{4}\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