00:01
Okay, for your question, it says an investor purchased three stocks for a one -week trading period.
00:07
The probabilities of a rise in the prices are 0 .8, 0 .7, and 0 .6, respectively.
00:14
So what i did was i named a three stocks, a, b, and c.
00:17
That'll help us organize this a little bit.
00:19
The probability that a will rise is 0 .8.
00:22
The probability b will rise is 0 .7.
00:25
C rise, 0 .6.
00:27
Then you have three questions.
00:28
The first question is the probability that all will fall in the next week.
00:34
That's a pretty straightforward probability.
00:36
All we need to do is calculate what is the probability of each of them falling individually, and then we can multiply those values together.
00:46
So the probability that a will fall will be 1 minus 0 .8 or 20%.
00:58
Probability that b will fall be 1 minus 0 .7 or 0 .3%, and the probability that c will fall would be 0 .4%.
01:12
And all you need to do to figure out the probability that all of them fall would be to multiply their individual probabilities together for falling.
01:25
So if i do that, 0 .2 times 0 .3 times 0 .4, it's going to end up being 0 .024.
01:33
So that is your probability that they all would fall.
01:37
Whoops.
01:40
0 .04.
01:43
All fall.
01:45
These other two questions that you have are a little bit more complex.
01:49
And to do them, i decided to make a tree diagram to organize all the different situations that can occur.
01:55
The first two branches of my tree diagram are for stock a.
02:00
The upper branch is representing a rise.
02:04
Point eight, the lower branch representing a fall point two.
02:09
Then we could look at, okay, that's event one, our first event.
02:14
This is our second event, stock b.
02:16
Stock b could rise point seven or drop point three point three for the probability of a fall.
02:24
Then i move on to the last stock.
02:27
So what you see is basically i'm repeating the probabilities for c at each of those branches because they're coming out of different scenarios to get to them.
02:38
The probability of at least two rise, and you just kind of look for the branches that would have a rise, at least two means we can have two rises or three rises.
02:53
So i could have a rise, b rise, and c rise.
02:58
That counts as a situation of something we are interested in, all three of them rows.
03:04
So let me highlight that result.
03:10
So 0 .336 represents all three of them rising.
03:16
We could have just a rise and b rise and c fall.
03:22
So that could be 0 .8 .7 times 0 .4.
03:29
And that would also be a scenario where we had two rise.
03:33
That was the 0 .8 rise and the 0 .7 rise.
03:36
And the point four didn't rise, the third stock.
03:43
And you continue to do this and work through the tree diagram, trying to find two.
03:47
We won't find any more where all three rise, but we can find more examples where two of them rise...