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There are two bags A and B. Bag A contains 5 blue balls and x red balls and bag B contains x blue balls and 8 red balls. If one ball is chosen at random from any one bag, then the probability that it is a red ball is 5/9. Find ‘x’ 
  • a)
    10
  • b)
    4
  • c)
    3
  • d)
    5
  • e)
    both (A) and (B)
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
There are two bags A and B. Bag A contains 5 blue balls and x red ball...

 x=10,4 
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Most Upvoted Answer
There are two bags A and B. Bag A contains 5 blue balls and x red ball...
Explanation:

Given information:
- Bag A contains 5 blue balls and x red balls
- Bag B contains x blue balls and 8 red balls
- Probability of choosing a red ball from any bag is 5/9

Probability of choosing a red ball from Bag A:
- Total number of balls in Bag A = 5 (blue balls) + x (red balls) = 5 + x
- Probability of choosing a red ball from Bag A = x / (5 + x)

Probability of choosing a red ball from Bag B:
- Total number of balls in Bag B = x (blue balls) + 8 (red balls) = x + 8
- Probability of choosing a red ball from Bag B = 8 / (x + 8)

Given probability:
- Probability of choosing a red ball from any bag = 5/9

Equating the probabilities:
- x / (5 + x) + 8 / (x + 8) = 5/9
- Solving this equation will give us the value of x

Solution:
- Solving the equation will yield x = 4
- Therefore, the correct answer is option 'E' which states that x = 4.
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