﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.00,0:00:04.00,Default,,0000,0000,0000,,We can compute this using the formula for conditional probability. Dialogue: 0,0:00:04.00,0:00:09.00,Default,,0000,0000,0000,,In this case what A is is the probability the coin toss is valid. Dialogue: 0,0:00:09.00,0:00:18.00,Default,,0000,0000,0000,,A is valid, and we know that the probability of A is equal to 0.99998. Dialogue: 0,0:00:18.00,0:00:21.00,Default,,0000,0000,0000,,What B is is the probability that it's heads. Dialogue: 0,0:00:21.00,0:00:29.00,Default,,0000,0000,0000,,So the probability of B is the probability of H, which is 0.49999. Dialogue: 0,0:00:29.00,0:00:32.00,Default,,0000,0000,0000,,Now we just have to plug these into the formula. Dialogue: 0,0:00:32.00,0:00:36.00,Default,,0000,0000,0000,,But what we need to use the formula is the probability of A intersect B. Dialogue: 0,0:00:36.00,0:00:42.00,Default,,0000,0000,0000,,And what A is the probability of A intersect B. What A is is valid. Dialogue: 0,0:00:42.00,0:00:46.00,Default,,0000,0000,0000,,Instead of heads and tails, what B is is heads. Dialogue: 0,0:00:46.00,0:00:52.00,Default,,0000,0000,0000,,If we intersect heads and tails with heads, we get tails. Dialogue: 0,0:00:52.00,0:00:57.00,Default,,0000,0000,0000,,We know the probability of tails is 0.49999. Dialogue: 0,0:00:57.00,0:01:04.00,Default,,0000,0000,0000,,That means using the formula we have the probability of tails, which is 0.49999, Dialogue: 0,0:01:04.00,0:01:07.00,Default,,0000,0000,0000,,which is the probability of A intersect B. Dialogue: 0,0:01:07.00,0:01:12.00,Default,,0000,0000,0000,,We're dividing that by the probability of A, Dialogue: 0,0:01:12.00,0:01:18.00,Default,,0000,0000,0000,,which is a valid event which is 0.99998. Dialogue: 0,0:01:18.00,0:01:20.00,Default,,0000,0000,0000,,We get 0.5. Dialogue: 0,0:01:20.00,0:01:23.00,Default,,0000,0000,0000,,I should note that this is not the case for real coin tosses. Dialogue: 0,0:01:23.00,0:01:28.00,Default,,0000,0000,0000,,There is no physical coin ever manufactured that has exactly Dialogue: 0,0:01:28.00,0:01:30.00,Default,,0000,0000,0000,,chances of landing on both sides. Dialogue: 0,0:01:30.00,0:01:34.00,Default,,0000,0000,0000,,In fact, with real coin tosses, at least with American currency, Dialogue: 0,0:01:34.00,0:01:39.00,Default,,0000,0000,0000,,there is a much higher percentage--much higher meaning close to 51% Dialogue: 0,0:01:39.00,0:01:43.00,Default,,0000,0000,0000,,rather than 50%--that the coin lands on the same side that it started on. Dialogue: 0,0:01:43.00,0:01:46.00,Default,,0000,0000,0000,,When we talk about mathematical coin tosses, Dialogue: 0,0:01:46.00,0:01:48.00,Default,,0000,0000,0000,,we're going to assume that there is no edge case Dialogue: 0,0:01:48.00,0:01:50.00,Default,,0000,0000,0000,,and that it's equally likely Dialogue: 0,0:01:50.00,0:01:53.00,Default,,0000,0000,0000,,that we have a uniform distribution and there are only 2 outcomes. Dialogue: 0,0:01:53.00,0:01:56.00,Default,,0000,0000,0000,,When we talk about mathematical coin tosses, Dialogue: 0,0:01:56.00,0:01:58.00,Default,,0000,0000,0000,,we're going to assume that we have a uniform distribution, Dialogue: 0,0:01:58.00,9:59:59.99,Default,,0000,0000,0000,,and there are only two outcomes.