Question

Download Solution PDF

A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green?

This question was previously asked in
UGC NET Computer Science (Paper 2) Dec 2018 Paper
Attempt in App
View all UGC NET Papers >
  1. 1/35
  2. 1/14
  3. 1/9
  4. 3/7

Answer (Detailed Solution Below)

Option 4 : 3/7
Free Tests
View all Free tests >
Free
UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins
Start Now

Detailed Solution

Download Solution PDF

Data:

red balls = 6  

green balls = 4

To Find:  The probability that two of the selected balls will be red and two will be green

Calculation:

Total balls = 6 + 4 = 10

4 balls from 10 balls can be selected in 10C4

2 red balls can be selected in 6C2 ways.

2 green balls from 4 green balls can be selected in 4C2 ways.

Probability that two selected balls will be red and two will be green =  

Important Point

Since red and green ball is asked, we have multiplied

Download Solution PDF
Latest UGC NET Updates

Last updated on Jun 12, 2025

-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.

-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.

-> The exam is conducted bi-annually - in June and December cycles.

-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions. 

-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.

Exams Tests Super Practice

More Introduction Questions

Q1.An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is
Q2.A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green?
Q3.Out of 8 gentlemen and 5 ladies, a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include at least 3 ladies?
Q4.Two events A and B with probability 0.5 and 0.7 respectively, have joint probability of 0.4 the probability that neither A or B happens is
Q5.If there are 4 addressed envelopes and 4 letters. Then, the chance that at least 1 letter is not mailed through proper envelope is
Q6.Three dices are thrown simultaneously. What is the probability that the sum of numbers is 15?
Q7.A box contains 25 balls of two colours, red and white. If the probability of picking a red ball at random is \(\frac25\), what is the probability of picking first ball red and second ball white without replacement?
Q8.Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is _____.
Q9.In a competition two persons, A and B wrote an exam. The probability of A's pass is 3/7 and the probability of B's pass is 3/5. What is the probability that only one of them is passed out?

More Probability Questions

Q1.A boy has 5 red balls, 3 white balls, and 2 yellow balls. What percent of balls are yellow?
Q2.In a batch Of 100 resistors Of 1kiloohm resistance, 80 numbers are within the required tolerance values and 11 numbers are below the required tolerance values, the remaining are above the required tolerance values. If two resistors are drawn one after the other without replacement, the probability of the first one drawn is below and the second one drawn is above the required tolerance value is 
Q3.There are three boxes. First box has 2 white, 3 black and 4 red balls. Second box has 3 white, 2 black and 2 red balls. Third box has 4 white, 1 black and 3 red balls. A box is chosen at random and 2 balls are drawn out of which 1 is white, and 1 is red. What is the probability that the balls came from first box?
Q4.If A, B, C are three mutually exclusive and exhaustive events such that if P(B) = \(\frac{3}{2}\)P(A) and P(C) = \(\frac{1}{2}\)P(B), then P(A) = _______
Q5.A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ________ (round off to two decimal places)
Q6.The value of a and b so that the following is probability mass function X: 0 1 2 P(X = x): 3a 3b 4b with mean 1.1, is:
Q7.Two data set of sizes 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 respectively. The standard deviation of combined data set of size 15 is
Q8.Probability that a leap year selected at random containing 53 Sundays, is equal to
Q9.If two events A and B such that P(A ∪ B) = \(\frac{7}{8}\) and P(A ∩ B) = \(\frac{1}{4}\) and P(A) = \(\frac{5}{8}\), then P\((\overline{A} ∪ \overline{B})\) = ?
Q10.If the life of mobile batteries is exponentially disturbed with parameter \(\lambda\) = 0.002 days, the probability that a battery will last more than 1500 days is:

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti real cash 2024 teen patti real cash teen patti master 51 bonus teen patti gold online master teen patti