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A box contains 5 white and 7 black balls. two successive drawn of 3 balls are made (i) with replacement (ii) without replacement . the probability that the first draw would produce white balls and the second draw would produce black balls are respectively
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Probability of Drawing White and Black Balls from a Box


Given Information:


  • Number of white balls in the box = 5

  • Number of black balls in the box = 7

  • Two successive draws are made

  • First draw should produce white balls

  • Second draw should produce black balls



Probability Calculation:


With Replacement:


  • Total number of balls in the box = 12

  • Probability of drawing a white ball in the first draw = 5/12

  • Probability of drawing a black ball in the second draw = 7/12

  • Probability of both events occurring = (5/12) * (7/12) = 35/144



Without Replacement:


  • Total number of balls in the box = 12

  • Probability of drawing a white ball in the first draw = 5/12

  • After first draw, there are 4 white balls and 7 black balls left in the box

  • Probability of drawing a black ball in the second draw = 7/11

  • Probability of both events occurring = (5/12) * (7/11) = 35/132



Conclusion:


  • The probability of drawing a white ball in the first draw and a black ball in the second draw is 35/144 with replacement and 35/132 without replacement.

  • The probability of drawing a white ball in the first draw and a black ball in the second draw is higher without replacement.

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A box contains 5 white and 7 black balls. two successive drawn of 3 balls are made (i) with replacement (ii) without replacement . the probability that the first draw would produce white balls and the second draw would produce black balls are respectively Related: Probability (Part - 2)?
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