[Script Info]
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[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.