Maths question from Social Forest Worker exam, 2026 by JKSSB
A bag contains 4 red, 3 blue, and 3 green balls. Three balls are drawn without replacement. What is the probability that exactly two balls are of the same colour and one is different?
Last updated Jul 21, 2026
Correct Answer:
Option D —
13/20
Here is the step-by-step breakdown using plain text without any mathematical symbols:
Step 1: Find the total number of ways to pick three balls
The bag contains four red, three blue, and three green balls, making a total of ten balls.
The number of ways to select any three balls out of ten without regard to order is one hundred twenty ways.
Step 2: Calculate the favorable ways for each color pair
We need three balls where exactly two share one color and the third ball is a different color.
Case 1: Two Red balls and one non-Red ball
Choosing two red balls out of four gives six ways.
Choosing one non-red ball from the remaining six balls (three blue and three green) gives six choices.
Combining these yields six times six, which equals thirty-six ways.
Case 2: Two Blue balls and one non-Blue ball
Choosing two blue balls out of three gives three ways.
Choosing one non-blue ball from the remaining seven balls (four red and three green) gives seven choices.
Combining these yields three times seven, which equals twenty-one ways.
Case 3: Two Green balls and one non-Green ball
Choosing two green balls out of three gives three ways.
Choosing one non-green ball from the remaining seven balls (four red and three blue) gives seven choices.
Combining these yields three times seven, which equals twenty-one ways.
Step 3: Calculate the total favorable ways and probability
Adding all favorable outcomes together: thirty-six plus twenty-one plus twenty-one gives seventy-eight favorable ways.
The probability is therefore seventy-eight out of one hundred twenty.
Dividing both seventy-eight and one hundred twenty by six reduces the fraction to thirteen out of twenty.
Correct Answer:
D) 13/20
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
