00:01
Okay, so in this question, we have two different options.
00:04
You have to make the choice between which option to use.
00:07
Option one has a 25 % chance of success, and it would make you $100 ,000, and then a 75 % chance of a loss of $300 ,000.
00:17
So let's first just calculate this expected value.
00:21
So we have a 25 % chance of making $100 ,000.
00:29
And then we have a 75 % chance.
00:46
So we're going to do minus 0 .75 % chance of losing 300 ,000.
01:07
So let's go ahead and calculate this.
01:10
So we have 0 .25 times 100 ,000.
01:15
That's 25 ,000.
01:17
Sorry, yeah, 25 ,000.
01:28
And then we have 0 .75 times 300 ,000.
01:33
So that's minus 225 ,000.
01:36
So this is really not good because, as you can see, we're going to be expected to lose money.
01:48
So the expected value, $25 ,000 minus $225 ,000 is negative $200 ,000.
01:58
So currently, if we're looking at just option one, we're going to be expected to lose $200 ,000.
02:12
Now let's calculate the expected value for the second option.
02:17
So option two has a 10 % chance of success.
02:20
So that's going to be 0 .1 times if we do win though or if we do have a success, it's going to make 600 ,000 minus a chance of failure is 0 .9 times 400 ,000.
02:50
I'm just going to put 400k because i'm running out of space, but i mean 400 ,000.
02:55
So let's do 0 .1 times 600 ,000.
03:00
And that's 60 ,000, minus 0 .9 times 4 ,000.
03:04
400 ,000.
03:07
And we get an expected value of negative 300 ,000.
03:32
So this one's even worse because you can see with option two, we're expected to lose about $300 ,000.
03:38
So first of all, if we're looking at these two expected values, okay, and we're assuming here that we don't know, we don't know which one's going to be better, right? and both of them have really low chances of success.
03:53
So overall, this option two is so much riskier.
04:00
You can make 600 ,000, but at the same time, if you have a fail, you lose $400 ,000, and that's more than losing the $300 ,000.
04:17
And then you look, on the other hand, we could have made $100 ,000 with option one, or made $300 ,000.
04:25
And then you look, on the other hand, we could have 600 ,000 with option two.
04:27
So option two is just a little bit riskier.
04:31
Second of all, if we look at the chances of success, we only have a 10 % chance of success for option two.
04:42
So just looking at the probability itself, we have a 10 % chance that we would be making money with option two.
04:51
And we have basically a 90 % chance of losing money, of losing.
04:57
$400 ,000 versus with option one we have a 10 % chance sorry 25 % chance of making $100 ,000 and only a 75 % chance of losing 300 ,000 which is still less.
05:11
So i think we're just operating under the assumption that most likely we're going to have a fail, right? it's more likely that we're going to have a fail than that we're going to have a success.
05:21
So if we're going to fail, then we would want to lose only 300 ,000 instead of 400 ,000.
05:28
Because we're really just basing it strictly on probability and not so much like an informed decision.
05:38
And then last, if you take a look at the expected value, once again, what we calculated, this is how much you can expect to make.
05:46
Both amounts are negative because there's such a high probability that we'd lose money, that we're kind of just expected to lose money, right? and going based of option one, we would be expected to only lose 200 ,000, whereas with option 2 ,000, we would be expected to lose 300 ,000.
06:07
Let's go ahead, since i guess they want a little bit more than expected value, let's look at this probability distribution.
06:14
Let's come up with a chart, because we can have a couple different cases.
06:23
So i'm just going to make this, let's see.
06:27
To make this side option one and either we have a success or we have a failure and um option two over here success and failure okay sorry i actually decided to do it without a chart for now so um let's do let's do the probability that you pick option one and it fails and then you pay and then you pick option, or sorry, you don't pick option two, but pick, sorry, i didn't mean to write pick.
07:21
And then option two is a success.
07:26
That's what actually happened here.
07:27
Let's find what is the probability of that occurring.
07:30
So the probability that, let's say we pick option one, the probability of it failing is going to be 0 .75.
07:48
And then we have times.
07:52
The probability that we would have had option two be a success is point one.
08:00
So we have 0 .75 times point 1.
08:07
That's 0 .075.
08:12
So i guess my chart would have worked earlier, but we'll kind of organize it later.
08:16
Okay, so that is about an 8 % chance that you would pick option one.
08:22
Option 1 doesn't work, but option 2 would work.
08:25
Now let's find the probability that we could, what's the, a different thing.
08:32
We could pick option one like we did and it could be a success and then option two could have been a failure.
08:50
So probability of option one being a success was 0 .25.
08:55
Probability of option two being a fail was 0 .9 .25 times 0 .9 is 0 .225 .9 is 0 .225.
09:10
All right.
09:22
Now the last thing you could have done if you picked option one is you could have picked a option one, it could have been a success, and then it could be actually that also option two would have been a success too.
09:44
And in that case, of course, you would have wished that you would have picked option two.
09:49
Okay, so we have probability option one is a success, point two five.
09:54
Probability option two is a success, point one.
09:57
So probability that they both actually end up being successes is 0 .25 times 0 .0 .0 .05.
10:10
Really small chance.
10:12
Like a 3 % chance that they would both be successful.
10:20
Now let's look at the other way around...
