What is the difference between the expected value of a lottery and the expected utility of a lot

What is the difference between the expected value of a...

Key Concepts

Expected Value

The expected value is a calculation that aggregates all possible numerical outcomes of a lottery, each weighted by its probability of occurrence. It represents the long-run average or mean outcome if the lottery were repeated many times and is calculated by summing the products of each outcome and its corresponding probability.

Utility Function

A utility function assigns a subjective value or level of satisfaction to different outcomes, reflecting an individual's preferences beyond their monetary or quantitative value. This function is often non-linear, capturing attitudes towards risk such as risk aversion or risk seeking.

Expected Utility

The expected utility of a lottery is computed by applying a utility function to each outcome before averaging, thereby incorporating an individual's risk preferences into the decision-making process. Unlike the expected value, which is purely statistical, expected utility reflects the perceived desirability of outcomes and helps to explain choices under uncertainty.

Transcript

00:01 Okay, so here the important bit is knowing the difference between a permutation and a combination.

00:08 For winning lottery ticket order does not matter.

00:10 So we want a combination, right, which is going to be equivalent to n choose r, where n is the total number of objects in the set, and for us, this is the 50 possible numbers, and r is the number we're choosing.

00:39 So it's going to give us n factorial over r factorial times n minus r factorial.

00:54 Okay, and so then the probability of the number of favorable outcomes over the number of possible outcomes is going to give us the probability that we would win.

01:21 Okay, so this is going to be equal to.

01:23 There's one favorable outcome, which is where all six.

01:25 Numbers are correct.

01:27 And the possible outcomes we determine here by doing a combination.

01:33 Okay, so that's going to be a combination where n is 50, the 50 possible numbers to choose from, and then we're choosing the six correct ones.

01:46 Okay, so this ends up being equal to six factorial times 50 minus 6 factorial over 50 factorial.

02:04 Okay, and if you calculate that out, it ends up being 1 over 15 ,890 ,000, and 700.

02:25 Okay, so then we'll use the complement rule to see that a probability of a loss is going to be equal to 1 minus the probability.

02:38 Of winning which is going to be equal to one minus this fraction here so as the one over 15 ,890 ,000 and 700 and that gives us 15 ,890 ,000 and that gives us 15 ,890 ,000 99 over 15 ,890 ,000...

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