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There are two containers, with one containing 4 Red and 3 Green balls and the other containing Blue and 4 Green balls. One bal is drawn at random form each container.The probability that one of the ball is Red and the other is Blue will be
- a)1/7
- b)9/49
- c)12/49
- d)3/7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
There are two containers, with one containing 4 Red and 3 Green balls ...
Ans. (c)
This question is part of UPSC exam. View all Mechanical Engineering courses
Most Upvoted Answer
There are two containers, with one containing 4 Red and 3 Green balls ...
Total number of case = (4+3) × (3+4) = 49
favourable case = 4C1 and 3C1 = 4×3 = 12
probability = 12 / 49
option C is correct
favourable case = 4C1 and 3C1 = 4×3 = 12
probability = 12 / 49
option C is correct
Community Answer
There are two containers, with one containing 4 Red and 3 Green balls ...
Problem:
There are two containers, one containing 4 Red and 3 Green balls and the other containing Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the ball is Red and the other is Blue will be
Solution:
To solve this problem, we need to find the probability of drawing one Red ball from the first container and one Blue ball from the second container.
Step 1: Determine the total number of balls in each container
- Container 1: 4 Red balls + 3 Green balls = 7 balls
- Container 2: 1 Blue ball + 4 Green balls = 5 balls
Step 2: Calculate the probability of drawing a Red ball from the first container
- Probability of drawing a Red ball from the first container = Number of Red balls / Total number of balls in the first container
- Probability of drawing a Red ball from the first container = 4 / 7
Step 3: Calculate the probability of drawing a Blue ball from the second container
- Probability of drawing a Blue ball from the second container = Number of Blue balls / Total number of balls in the second container
- Probability of drawing a Blue ball from the second container = 1 / 5
Step 4: Calculate the overall probability
To find the probability that one of the ball is Red and the other is Blue, we need to multiply the probabilities of drawing a Red ball from the first container and a Blue ball from the second container.
- Overall probability = Probability of drawing a Red ball from the first container * Probability of drawing a Blue ball from the second container
- Overall probability = (4 / 7) * (1 / 5)
- Overall probability = 4 / 35
Step 5: Simplify the overall probability
To simplify the overall probability, we can divide both the numerator and denominator by 4.
- Overall probability = (4 / 4) / (35 / 4)
- Overall probability = 1 / (35 / 4)
- Overall probability = 1 / (8.75)
- Overall probability = 4 / 35
Conclusion:
The probability that one of the ball is Red and the other is Blue is 4 / 35, which is equivalent to option 'C' (12/49) in the given options.
There are two containers, one containing 4 Red and 3 Green balls and the other containing Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the ball is Red and the other is Blue will be
Solution:
To solve this problem, we need to find the probability of drawing one Red ball from the first container and one Blue ball from the second container.
Step 1: Determine the total number of balls in each container
- Container 1: 4 Red balls + 3 Green balls = 7 balls
- Container 2: 1 Blue ball + 4 Green balls = 5 balls
Step 2: Calculate the probability of drawing a Red ball from the first container
- Probability of drawing a Red ball from the first container = Number of Red balls / Total number of balls in the first container
- Probability of drawing a Red ball from the first container = 4 / 7
Step 3: Calculate the probability of drawing a Blue ball from the second container
- Probability of drawing a Blue ball from the second container = Number of Blue balls / Total number of balls in the second container
- Probability of drawing a Blue ball from the second container = 1 / 5
Step 4: Calculate the overall probability
To find the probability that one of the ball is Red and the other is Blue, we need to multiply the probabilities of drawing a Red ball from the first container and a Blue ball from the second container.
- Overall probability = Probability of drawing a Red ball from the first container * Probability of drawing a Blue ball from the second container
- Overall probability = (4 / 7) * (1 / 5)
- Overall probability = 4 / 35
Step 5: Simplify the overall probability
To simplify the overall probability, we can divide both the numerator and denominator by 4.
- Overall probability = (4 / 4) / (35 / 4)
- Overall probability = 1 / (35 / 4)
- Overall probability = 1 / (8.75)
- Overall probability = 4 / 35
Conclusion:
The probability that one of the ball is Red and the other is Blue is 4 / 35, which is equivalent to option 'C' (12/49) in the given options.
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