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Probability, SM-Bank 089

The fish in a pond are to be removed for the pond to be cleaned. There are 4 different types of coloured carp in the pond.

Calculate the probability that the first carp captured is orange, given the probability of capturing:

  • a red carp is \(\dfrac{2}{9}\)
  • a white carp is \(\dfrac{1}{6}\) and
  • a mulit-coloured carp is \(\dfrac{5}{12}\).  (2 marks)
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\(\dfrac{7}{36}\)

Show Worked Solution

\(\text{The sum of all probabilities in an event = 1}\)

\(P\text{(Orange)}\) \(=1-\Bigg(\dfrac{2}{9}+\dfrac{1}{6}+\dfrac{5}{12}\Bigg)\)
  \(=1-\Bigg(\dfrac{8}{36}+\dfrac{6}{36}+\dfrac{15}{36}\Bigg)\)
  \(=1-\dfrac{29}{36}=\dfrac{7}{36}\)