00:01
Okay, so we're flipping five coins and we're going to be finding some different probabilities based off.
00:06
So these are going to kind of start off a little bit easier in terms of conceptualize and then we'll kind of work our way, some harder ones.
00:12
So first of all, we think about all heads.
00:15
The probability of flipping a heads, our normal coin is 50 -50, one -half.
00:20
We have this probability of one half.
00:24
That's on the first one.
00:26
Each coin is going to have, each time we flip it, i should say, it's going to have a probability of one half.
00:32
So to get heads five times in a row, we would just multiply all these.
00:38
Half, one half, half, half, half, half.
00:43
And when we multiply these, we get one over 32.
00:47
That's the probability.
00:50
Okay.
00:51
But now we're still some different cases.
00:55
We want to accept one.
01:00
So let's think of the possibilities.
01:01
If we want one, we could flip the head in the first one and have all the fields.
01:10
Or we could have all tails otherwise.
01:15
Or we could flip it in third.
01:17
One or the fourth one or the fifth one so there are five possible instances of flipping one head and the rest here so we're gonna have a five in our design is a coin flip so we multiply all together means 32 possible combinations of head the probability of one head is five on the three we talked about the five different ways heads on the first one heads on the second heads on the third heads on the fourth heads on the fifth and with those combinations is the record or flip the table.
02:04
So there's only fine about a free.
02:08
We could apply this new one to our tables.
02:13
Now, we're going to value some combinatorics finding how many ways to choose two spaces out of five.
02:28
You do that, i'm going to be doing it's not any kind of factor.
02:32
So let's draw our five spaces again.
02:35
Two tails.
02:35
Okay, well, flip one and two could be tails.
02:40
We're just assuming the rest of you guys are done.
02:42
Or we can have one in three, one in four, one in five.
02:49
Then we can have two and three, two and four, two and five.
02:57
Scroll down and get all these possibilities in here, because we have quite a number of them.
03:12
Actually, what i'm going to do, i'm going to run up there.
03:14
You see what i'm doing as far as picking the spots, it's just kind of a matter of listing all the comments.
03:19
So here we go, one, two, one, three, one, four, one, five.
03:24
2, 3, 24, 2, 5, 3, 4, 5, and then 4, 5.
03:31
So these are the spot where they are.
03:33
You'll notice there are 10 different places, 10 different instances to be exactly 2x in these positions.
03:41
And we talk about the possibilities, and we can simplify that a little bit.
03:52
Okay.
03:54
Now, at least one tail.
03:57
Okay, so at least, usually not one tail all the way up.
04:02
Here, sometimes we want to do complementary, where we don't want to count how many times we can get something, we want to count we can't get something.
04:10
Here, it's going to be easier to do that because at least one means the only thing we don't want to go take it.
04:18
So that would mean we have five heads more.
04:22
And there's only one way of doing it.
04:23
Look at five times and each time.
04:25
So this is our part a here.
04:30
That's the only possibility we don't know.
04:34
So what we would do, for complimentary, we do one line.
04:39
So 1 minus 1 over 3 .1 is 32 over 32.
04:44
So we subtract it and we get 31 over 3.
04:50
So we have very good odds.
04:53
If we flip a 5 point, we get at least 1.
04:57
Only chance, the only way we can't is 5.
05:00
All right, so let's scroll down a little bit here...