Mrs Okafor divides her monthly income between four spending categories: rent, food, transport and savings. The probability she needs to adjust the rent cate...
Question 1 Report
Mrs Okafor divides her monthly income between four spending categories: rent, food, transport and savings. The probability she needs to adjust the rent category next month is \(0.15\), and the probability she needs to adjust the food category is \(0.4\). These two adjustments cannot both happen in the same month.
- Work out the probability that she needs to adjust either the rent category or the food category. (2)
- Work out the probability that she needs to adjust neither category. (2)
Answer Details
The question states the two adjustments cannot both happen in the same month, so they are mutually exclusive and their probabilities are simply added for "either" and their sum subtracted from 1 for "neither".
- [2] \[ P(\text{rent or food}) = 0.15 + 0.4 = 0.55 \]
- [2] \[ P(\text{neither}) = 1 - 0.55 = 0.45 \]
Adding the two probabilities directly is only valid because the events are stated to be mutually exclusive; without that condition, an overlap would need to be subtracted, as in independent-event or Venn diagram questions.
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