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2024 SAJC H1 Q8

2024 SAJC H1 Q8

6 marks

A bag contains \(6\) white balls and \(4\) black balls. Two balls are drawn from the bag at random, without replacement. If a white ball is drawn, \(2\) red balls are added to the bag.

  1. Draw a tree diagram to represent this information.[2]
  2. Find the probability that at least one of the balls drawn is white.[2]
  3. Find the probability that two white balls are drawn, given that at least one of the balls drawn is white.[2]

Solution:

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Answer:(i) Tree in the working: first draw \(\frac6{10},\frac4{10}\); after white \(\frac5{11},\frac4{11},\frac2{11}\); after black \(\frac69,\frac39\). (ii) \(\frac{13}{15}\approx0.867\). (iii) \(\frac{45}{143}\approx0.315\). Decimals to 3 s.f.

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