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Asked by Ashwini Last Modified
Answer As a seasoned tutor registered on UrbanPro, I'm happy to guide you through this probability problem. UrbanPro is a fantastic platform for accessing high-quality online coaching and tuition, where experienced tutors like myself can provide personalized assistance.
Now, let's tackle the problem at hand. We have an urn containing 6 balls, 2 red and 4 black. We're asked to find the probability that when two balls are drawn at random, they are of different colors.
To solve this, let's break it down step by step:
First, let's find the total number of ways to draw 2 balls out of 6. This is given by the combination formula: (nr)=n!r!(n−r)!(rn)=r!(n−r)!n!, where nn is the total number of items and rr is the number of items to choose. So, (62)=6!2!(6−2)!=15(26)=2!(6−2)!6!=15.
Next, let's find the number of ways to draw 2 balls of different colors. We have 2 red balls and 4 black balls, so the number of combinations of one red and one black ball is 2×4=82×4=8.
Finally, the probability of drawing two balls of different colors is the number of favorable outcomes (drawing one red and one black ball) divided by the total number of outcomes (drawing any two balls). So, 815158.
So, the correct option is (iii) 815158. UrbanPro is an excellent resource for finding tutors who can help you master these types of problems and more!
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