Question
Download Solution PDFFirst bag contains 5 white and 4 black balls. Second bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
First bag contains 5 white and 4 black balls.
Second bag contains 7 white and 9 black balls.
Formula Used:
Probability = Number of favorable outcomes / Total number of outcomes
Calculation:
Probability of transferring a white ball from the first bag to the second bag = 5/9
After transferring a white ball, the second bag will have 8 white balls and 9 black balls.
Probability of drawing a white ball from the second bag = 8/17
Probability of transferring a black ball from the first bag to the second bag = 4/9
After transferring a black ball, the second bag will have 7 white balls and 10 black balls.
Probability of drawing a white ball from the second bag = 7/17
Total Probability:
\(\frac{5}{9} \times \frac{8}{17} + \frac{4}{9} \times \frac{7}{17}\)
⇒ \(\frac{5}{9} \times \frac{8}{17} + \frac{4}{9} \times \frac{7}{17} = \frac{40}{153} + \frac{28}{153} = \frac{68}{153}\)
⇒ \(\frac{4}{9}\)
The probability that the ball drawn is white is \(\frac{4}{9}\) .
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