WEBVTT 00:00:00.000 --> 00:00:04.000 We can compute this using the formula for conditional probability. 00:00:04.000 --> 00:00:09.000 In this case what A is is the probability the coin toss is valid. 00:00:09.000 --> 00:00:18.000 A is valid, and we know that the probability of A is equal to 0.99998. 00:00:18.000 --> 00:00:21.000 What B is is the probability that it's heads. 00:00:21.000 --> 00:00:29.000 So the probability of B is the probability of H, which is 0.49999. 00:00:29.000 --> 00:00:32.000 Now we just have to plug these into the formula. 00:00:32.000 --> 00:00:36.000 But what we need to use the formula is the probability of A intersect B. 00:00:36.000 --> 00:00:42.000 And what A is the probability of A intersect B. What A is is valid. 00:00:42.000 --> 00:00:46.000 Instead of heads and tails, what B is is heads. 00:00:46.000 --> 00:00:52.000 If we intersect heads and tails with heads, we get tails. 00:00:52.000 --> 00:00:57.000 We know the probability of tails is 0.49999. 00:00:57.000 --> 00:01:04.000 That means using the formula we have the probability of tails, which is 0.49999, 00:01:04.000 --> 00:01:07.000 which is the probability of A intersect B. 00:01:07.000 --> 00:01:12.000 We're dividing that by the probability of A, 00:01:12.000 --> 00:01:18.000 which is a valid event which is 0.99998. 00:01:18.000 --> 00:01:20.000 We get 0.5. 00:01:20.000 --> 00:01:23.000 I should note that this is not the case for real coin tosses. 00:01:23.000 --> 00:01:28.000 There is no physical coin ever manufactured that has exactly 00:01:28.000 --> 00:01:30.000 chances of landing on both sides. 00:01:30.000 --> 00:01:34.000 In fact, with real coin tosses, at least with American currency, 00:01:34.000 --> 00:01:39.000 there is a much higher percentage--much higher meaning close to 51% 00:01:39.000 --> 00:01:43.000 rather than 50%--that the coin lands on the same side that it started on. 00:01:43.000 --> 00:01:46.000 When we talk about mathematical coin tosses, 00:01:46.000 --> 00:01:48.000 we're going to assume that there is no edge case 00:01:48.000 --> 00:01:50.000 and that it's equally likely 00:01:50.000 --> 00:01:53.000 that we have a uniform distribution and there are only 2 outcomes. 00:01:53.000 --> 00:01:56.000 When we talk about mathematical coin tosses, 00:01:56.000 --> 00:01:58.000 we're going to assume that we have a uniform distribution, 00:01:58.000 --> 99:59:59.999 and there are only two outcomes.