2024 BTYSS P1 Q19

2024 BTYSS P1 Q19

Secondary 4
6 marks

A bag contains \(9\) red balls and \(7\) yellow balls. Two balls are taken from the bag at random, one after the other without replacement.

The diagram shows part of the probability tree.

\((\quad)\)
Red
\(\dfrac{7}{16}\)
Yellow
\((\quad)\)
Red
\((\quad)\)
Yellow
\((\quad)\)
Red
\((\quad)\)
Yellow
First ball
Second ball
  1. Complete the probability tree.[2]
  2. Find the probability that
    1. the second ball is yellow,[1]
    2. at least one ball is red.[1]
  3. A third ball is now taken out at random.
    Calculate the probability that he does not have \(3\) balls of the same colour.[2]

Solution:

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Answer:(a) First red: \(\dfrac{9}{16}\); after red: \(\dfrac{8}{15},\dfrac{7}{15}\); after yellow: \(\dfrac{9}{15},\dfrac{6}{15}\). (b)(i) \(\dfrac{7}{16}\) (ii) \(\dfrac{33}{40}\) (c) \(\dfrac{63}{80}\)

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