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A bag X contains 3 white and 2 black balls. Another bag Y contains 2 white and 4 black balls. A bag and a ball out of it are picked at random. Find the probability that the ball is of white colour.
- a)1/3
- b)7/15
- c)4/13
- d)1/2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A bag X contains 3 white and 2 black balls. Another bag Y contains 2 w...
Understanding the Problem
To find the probability that a randomly chosen ball is white, we need to consider both bags and their contents.
Contents of the Bags
- Bag X: 3 white balls, 2 black balls
- Bag Y: 2 white balls, 4 black balls
Step 1: Calculate Total Balls in Each Bag
- Total balls in Bag X = 3 + 2 = 5
- Total balls in Bag Y = 2 + 4 = 6
Step 2: Calculate Total Probability of Choosing Each Bag
Since there are two bags, the probability of choosing either bag is:
- P(Bag X) = 1/2
- P(Bag Y) = 1/2
Step 3: Calculate Probability of Picking a White Ball from Each Bag
- For Bag X:
- P(White | Bag X) = Number of white balls in Bag X / Total balls in Bag X
- P(White | Bag X) = 3/5
- For Bag Y:
- P(White | Bag Y) = Number of white balls in Bag Y / Total balls in Bag Y
- P(White | Bag Y) = 2/6 = 1/3
Step 4: Use Total Probability Theorem
The total probability of picking a white ball is:
P(White) = P(Bag X) * P(White | Bag X) + P(Bag Y) * P(White | Bag Y)
Calculating this gives:
P(White) = (1/2 * 3/5) + (1/2 * 1/3)
P(White) = (3/10) + (1/6)
Finding a common denominator (30):
P(White) = (9/30) + (5/30) = 14/30 = 7/15
Final Answer
Thus, the probability that the ball picked is white is 7/15, which corresponds to option 'B'.
To find the probability that a randomly chosen ball is white, we need to consider both bags and their contents.
Contents of the Bags
- Bag X: 3 white balls, 2 black balls
- Bag Y: 2 white balls, 4 black balls
Step 1: Calculate Total Balls in Each Bag
- Total balls in Bag X = 3 + 2 = 5
- Total balls in Bag Y = 2 + 4 = 6
Step 2: Calculate Total Probability of Choosing Each Bag
Since there are two bags, the probability of choosing either bag is:
- P(Bag X) = 1/2
- P(Bag Y) = 1/2
Step 3: Calculate Probability of Picking a White Ball from Each Bag
- For Bag X:
- P(White | Bag X) = Number of white balls in Bag X / Total balls in Bag X
- P(White | Bag X) = 3/5
- For Bag Y:
- P(White | Bag Y) = Number of white balls in Bag Y / Total balls in Bag Y
- P(White | Bag Y) = 2/6 = 1/3
Step 4: Use Total Probability Theorem
The total probability of picking a white ball is:
P(White) = P(Bag X) * P(White | Bag X) + P(Bag Y) * P(White | Bag Y)
Calculating this gives:
P(White) = (1/2 * 3/5) + (1/2 * 1/3)
P(White) = (3/10) + (1/6)
Finding a common denominator (30):
P(White) = (9/30) + (5/30) = 14/30 = 7/15
Final Answer
Thus, the probability that the ball picked is white is 7/15, which corresponds to option 'B'.
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A bag X contains 3 white and 2 black balls. Another bag Y contains 2 white and 4 black balls. A bag and a ball out of it are picked at random. Find the probability that the ball is of white colour.a)1/3b)7/15c)4/13d)1/2Correct answer is option 'B'. Can you explain this answer?
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