You buy a lottery ticket to a lottery that costs 10 per...

You buy a lottery ticket to a lottery that costs $\$ 10$ per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $\$ 500$ prize, two $\$ 100$ prizes, and four $\$ 25$ prizes. Find your expected gain or loss.

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Key Concepts

Expected Value

The expected value is a key concept in probability that represents the average outcome anticipated when an experiment (or random process) is repeated many times. It is calculated by multiplying each possible outcome by its probability and then summing all these products, providing insight into the long-term behavior of the experiment.

Probability Distribution

A probability distribution describes how probabilities are assigned to each outcome in a set of possible outcomes. It is essential for evaluating scenarios in probability and statistics because it quantifies the chance of each event occurring, which is necessary to compute measures like the expected value.

Net Gain or Loss

Net gain or loss refers to the overall profit or deficit resulting from a particular decision or investment after accounting for costs. In problems involving monetary outcomes, like lottery scenarios, it is obtained by subtracting the initial expense from the winnings for each outcome.

Sample Space

The sample space is the complete set of all possible outcomes in a random experiment. It serves as the framework for determining the probabilities associated with each outcome, and it is fundamental for constructing probability distributions and calculating expected values.

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