Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of $3.3 million per year. If sales are 'so so' they can make a profit of $2.3 million per year. Finally, if sales are low they can lose $1.35 million per year. The probability that sales will be high is 0.55. The probability that sales will be 'so so' is 0.15. Calculate the expected profit for the product (in $ millions per year) to two decimal places.
Question
Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of 2.3 million per year. Finally, if sales are low they can lose millions per year) to two decimal places.
Solution
The expected profit is calculated by multiplying each possible profit by the probability of that profit occurring, and then summing these values.
So, the expected profit E[P] is given by:
E[P] = (Profit_High * P_High) + (Profit_SoSo * P_SoSo) + (Profit_Low * P_Low)
We know that the Profit_High is 2.3 million, and Profit_Low is -$1.35 million (a loss is represented as a negative profit). We also know that P_High is 0.55 and P_SoSo is 0.15.
The probability of low sales, P_Low, is not given, but we know that the sum of all probabilities must be 1, so we can calculate P_Low as 1 - P_High - P_SoSo = 1 - 0.55 - 0.15 = 0.30.
Substituting these values into the formula gives:
E[P] = (3.3 * 0.55) + (2.3 * 0.15) + (-1.35 * 0.30) = 1.815 + 0.345 - 0.405 = 1.755
So, the expected profit is $1.755 million per year, to two decimal places.
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