Question

an entrepreneur has invested in four startups. if the startup makes profit, it will yield respective profits of 10,20,30 and 40 (in units of lakh). on the other hand, for each startup the entrepreneur may not gain profit, he will incur a loss of 3(in units of lakh). if the probabilities that the entrepreneur will make profits from these startups are, respectively, 0.2,0.3,0.4, and 0.1, what is the expected total profit (in lakhs)?

Answer 1

The expected total profit for the entrepreneur from all four startups is 15 lakhs, calculated by summing up the individual expected profits or losses from each startup.

Step-by-step explanation:

To find the expected total profit for the entrepreneur who has invested in four startups, we calculate the expected profit or loss for each startup and then sum them up. The expected value is calculated by multiplying the profit (or loss) with the probability of that outcome. Here's the calculation for each startup:

1. Startup 1: (0.2 * 10) + (0.8 * -3) = 2 - 2.4 = -0.4 (lakhs)
2. Startup 2: (0.3 * 20) + (0.7 * -3) = 6 - 2.1 = 3.9 (lakhs)
3. Startup 3: (0.4 * 30) + (0.6 * -3) = 12 - 1.8 = 10.2 (lakhs)
4. Startup 4: (0.1 * 40) + (0.9 * -3) = 4 - 2.7 = 1.3 (lakhs)

Adding the expected values from each startup, we get:

-0.4 + 3.9 + 10.2 + 1.3 = 15 (lakhs)

Therefore, the expected total profit for the entrepreneur from all four startups is 15 lakhs.

Answer 2

To calculate the expected total profit, multiply the profits of each startup by their respective probabilities of making a profit. Subtract the losses incurred for startups that don't make a profit. Add up all the expected profits to find the total expected profit. The expected total profit is 15 lakhs.

Step-by-step explanation:

To calculate the expected total profit, we need to multiply the profits of each startup by their respective probabilities of making a profit. If the startup makes a profit, the entrepreneur will gain the respective profit. If the startup incurs a loss, the entrepreneur will lose 3 units (lakhs). Here is how we calculate the expected total profit:

1. Startup 1: Expected profit = (0.2 * 10) + (0.8 * -3) = 2 - 2.4 = -0.4 (lakhs)
2. Startup 2: Expected profit = (0.3 * 20) + (0.7 * -3) = 6 - 2.1 = 3.9 (lakhs)
3. Startup 3: Expected profit = (0.4 * 30) + (0.6 * -3) = 12 - 1.8 = 10.2 (lakhs)
4. Startup 4: Expected profit = (0.1 * 40) + (0.9 * -3) = 4 - 2.7 = 1.3 (lakhs)
5. Total expected profit = -0.4 + 3.9 + 10.2 + 1.3 = 15 (lakhs)

The expected total profit is 15 lakhs.