A dealer has a stock of 15 gold coins out of which 6 are...

A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeits?

Options

A $\frac{1}{91}$
B $\frac{4}{91}$
C $\frac{6}{91}$
D $\frac{15}{91}$

Correct answer

A. $\frac{1}{91}$

Step-by-step solution

Number of ways of picking 4 counterfeits gold coins out of 6 counterfeits coins

={ }^6 C_4

Number of ways of picking 4 coins out of 15 gold coins

={ }^{15} C_4\therefore

Required probability

=\frac{{ }^6 C_4}{{ }^{15} C_4}=\frac{15}{15 \times 7 \times 13}=\frac{1}{91}

Practice Probability on Quantrex Academy →

More from Probability

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