00:02
Okay, here's a formula that we could use.
00:05
This is the formula for conditional probability.
00:09
It says the probability of b given a equals the probability of a and b, both conditions being met, divided by the probability of a.
00:25
So we could use that formula to answer this question.
00:30
And with three coins being flipped, we can make it easier, or maybe you know a better way, but i like this way, of just listing out every possible scenario.
00:55
So i can get three heads, i could flip heads, heads, tails, i could flip heads, tails, heads, i could flip heads, tails, tails, i could flip tails first, and then i could flip two heads, i could flip tails first, and then i could flip heads, and then i could flip tails, i could flip two tails first, and then heads, or i could flip all three tails.
01:28
Okay, so you can check, but that is every possible thing that could happen with three coin flips.
01:36
So we can take a close look at these different conditions.
01:41
So the question is, what's the probability that at least two heads will occur, that's our b condition, given that at most two heads have occurred? so a is at most two heads, and b is at least two heads.
02:25
Okay, so i'm going to use a red arrow for everything that meets condition a.
02:34
So at most two heads have occurred.
02:38
So first one meets that condition, no heads have occurred.
02:42
Second one's good, one head, one head, two heads, because it says at most two heads, i've got two heads, one head, two heads, two heads, oh, three heads.
02:56
That one's out, because it says at most two heads.
03:01
Okay, so notice that seven out of the eight have at most two heads.
03:08
So i could say the probability of a is seven out of eight.
03:15
Okay, now i'll use a blue arrow for condition b, at least two heads.
03:22
Okay, so looking at the first one, zero heads, no good.
03:27
Second one, one head, no good.
03:30
Third one, one head, no good.
03:33
Fourth one, at least two heads.
03:36
It's got two heads, so that one's good.
03:39
Next one, no good.
03:41
Next one, good, good...