Probability Perm/Comb. (1 Viewer)

moderntortoisecat

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B ox a contains six white and four black balls. box b contains two white and two black balls. from box a two balls are selected at random and placed in box b. two balls are then selected at random from box b. what is the probability that exactly one of these two balls are white?
 

gooner

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To solve this problem, we'll break it down into steps and consider the different scenarios that could happen, based on the selection of balls from Box A to Box B and then the selection from Box B.

Step 1: Selection from Box A to Box B
Initially, Box A contains 6 white and 4 black balls, and Box B contains 2 white and 2 black balls.
When two balls are selected from Box A and placed into Box B, there are three possible outcomes:
  1. Two white balls are selected from Box A: Probability = 6/10 * 5/9
  2. One white and one black ball are selected from Box A: Probability = 6/10 * 4/9 + 4/10 * 6/9
  3. Two black balls are selected from Box A: Probability = 4/10 * 3/9
Step 2: Selection from Box B
After the transfer, depending on which balls were added, we will have different compositions of Box B and thus different probabilities for selecting exactly one white ball out of two selected balls.
  1. If two white balls were added to Box B: Box B will have 4 white and 2 black balls. The probability of selecting exactly one white ball is given by selecting one white out of four and one black out of two.
  2. If one white and one black ball were added to Box B: Box B will have 3 white and 3 black balls. The probability of selecting exactly one white ball is given by selecting one white out of three and one black out of three, or the reverse.
  3. If two black balls were added to Box B: Box B will have 2 white and 4 black balls. The probability of selecting exactly one white ball is given by selecting one white out of two and one black out of four.
∴ The probability that exactly one of the two balls selected from Box B is white is approximately 56.9%
 

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