Mamma temte bakes six pies a day that cost $2. on 15% of the days she sells 3 pies, on 30% of the days she sells 4. On 55% of the days she sells six pies, if mama temte sells her pies for $6 each, what is her expected profit for a days worth of pies?[assuming extras will be given away]
67
To calculate Mama Temte's expected profit for a day's worth of pies, we need to determine the number of pies she sells each day and then calculate the profit for each scenario.
Let's start with the given information:
- On 15% of the days, Mama Temte sells 3 pies.
- On 30% of the days, Mama Temte sells 4 pies.
- On 55% of the days, Mama Temte sells 6 pies.
Next, we need to calculate the profit for each scenario:
- Selling 3 pies: On these days, Mama Temte's revenue is $6 * 3 = $18. However, since we know that extras will be given away, there is no additional profit from selling 3 pies. Therefore, the profit is $0.
- Selling 4 pies: On these days, Mama Temte's revenue is $6 * 4 = $24. Again, considering that extras will be given away, the profit from selling 4 pies is $24 - ($2 * 4) = $24 - $8 = $16.
- Selling 6 pies: On these days, Mama Temte's revenue is $6 * 6 = $36. Taking into account the cost of the pies, the profit from selling 6 pies is $36 - ($2 * 6) = $36 - $12 = $24.
Now, we need to calculate the expected profit based on the probabilities of each scenario occurring:
- Probability of selling 3 pies = 15% = 0.15
- Probability of selling 4 pies = 30% = 0.30
- Probability of selling 6 pies = 55% = 0.55
To calculate the expected profit:
Expected profit = (Profit from selling 3 pies * Probability of selling 3 pies) + (Profit from selling 4 pies * Probability of selling 4 pies) + (Profit from selling 6 pies * Probability of selling 6 pies)
Expected profit = ($0 * 0.15) + ($16 * 0.30) + ($24 * 0.55)
Expected profit = $0 + $4.8 + $13.2
Expected profit = $18
Therefore, Mama Temte's expected profit for a day's worth of pies, considering giving away extras, is $18.