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In a community garden in Melbourne, 83 plots are used for growing vegetables, and 19 plots are used for both vegetables and herbs. Of the 19 plots that grow herbs, 14 also grow vegetables.
If a plot is selected at random and is known to grow herbs, what is the probability that it also grows vegetables? Express your answer as an exact fraction.
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Worked solution
- The problem states that 19 plots grow herbs, and 14 of these also grow vegetables. This means that given a plot grows herbs, we are to find the probability it also grows vegetables.
- Conditional probability is defined as P(A|B) = P(A and B) / P(B). Here, A is 'grows vegetables', B is 'grows herbs'. We are given that 14 plots grow both vegetables and herbs, and 19 plots grow herbs.
- The number of plots that grow both vegetables and herbs is 14. The total number of plots that grow herbs is 19. Therefore, the probability that a herb-growing plot also grows vegetables is 14 / 19.
- The fraction 14/19 is already in simplest form because 14 and 19 share no common factors other than 1 (19 is prime and does not divide 14).
- No further simplification or conversion is needed. The probability is exactly 14/19.
Reference answer: 14/19
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