GATE EC 2025 Set 1 — Question 13
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Engineering Mathematics → Probability → Combinatorial Probability
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Question
A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?
Correct answer
(A) 2/3
Solution
Total number of balls = 2 Red + 2 Blue = 4 balls.
We are drawing 2 balls randomly without replacement.
Total number of ways to draw 2 balls from 4 is .We want the probability that the two balls drawn have different colours, which means one Red ball and one Blue ball.
Number of ways to draw 1 Red ball from 2 Red balls = .
Number of ways to draw 1 Blue ball from 2 Blue balls = .
Number of ways to draw 1 Red and 1 Blue ball = .Probability = .Therefore, the probability that the two balls drawn have different colours is .
We are drawing 2 balls randomly without replacement.
Total number of ways to draw 2 balls from 4 is .We want the probability that the two balls drawn have different colours, which means one Red ball and one Blue ball.
Number of ways to draw 1 Red ball from 2 Red balls = .
Number of ways to draw 1 Blue ball from 2 Blue balls = .
Number of ways to draw 1 Red and 1 Blue ball = .Probability = .Therefore, the probability that the two balls drawn have different colours is .
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