A box contains 5 black and 8 white balls. A ball is removed and replaced by two of the other color and then a second ball is drawn. Calculate:

(i) The probability that the second ball is white.

(ii) The probability that both balls drawn are the same colour.

  • $\begingroup$ There are 4 possible patterns with different probabilities: BB, WB, BW, WW. What happens if you consider each of them? $\endgroup$ – Henry Nov 8 at 13:54
  • $\begingroup$ I can work out each pattern, but for the 1st question, I have the formula for conditional probability, but I'm not sure how to calculate the 1st event? $\endgroup$ – Michael O' Driscoll Nov 8 at 13:55
  • $\begingroup$ So, to answer your hint, for BB, if Black is drawn, 2 whites are added, then another black is drawn, if W, then 2B added, then B is drawn...etc? $\endgroup$ – Michael O' Driscoll Nov 8 at 13:57
  • $\begingroup$ That was not quite my hint. What is the probability that Black was drawn first and Black drawn second, i.e. BB? I would presume $\frac{5}{5+8} \times \frac{4}{4+10}$. Can you do the same for the other three patterns? The probability that the second ball is white is the probability of BW plus the probability of WW. $\endgroup$ – Henry Nov 8 at 14:00

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