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Dialogue: 0,0:00:00.00,0:00:07.00,Default,,0000,0000,0000,,What have you learned? Well, to flip a coin n times one for k small or equal to n.
Dialogue: 0,0:00:07.00,0:00:11.00,Default,,0000,0000,0000,,We ask the probability--what are the chance it comes up heads k times.
Dialogue: 0,0:00:11.00,0:00:16.00,Default,,0000,0000,0000,,For any coin, with the probability of heads equals to all caps P,.
Dialogue: 0,0:00:16.00,0:00:23.00,Default,,0000,0000,0000,,we now get the following formula: n!/(n-k)!*k!.
Dialogue: 0,0:00:23.00,0:00:26.00,Default,,0000,0000,0000,,These are the total number of outcomes that have this property.
Dialogue: 0,0:00:26.00,0:00:28.00,Default,,0000,0000,0000,,And then this one has the following probability:
Dialogue: 0,0:00:28.00,0:00:39.00,Default,,0000,0000,0000,,P to the k, this was the (0.8)⁹ before times (1-p) to the n-k,
Dialogue: 0,0:00:39.00,0:00:43.00,Default,,0000,0000,0000,,which is the remaining 3 over here in this example.
Dialogue: 0,0:00:43.00,0:00:47.00,Default,,0000,0000,0000,,So, this formula is the probability of what's call the binomial distribution
Dialogue: 0,0:00:47.00,0:00:53.00,Default,,0000,0000,0000,,and really was this is the accumulated outcome of many identical coin flips,
Dialogue: 0,0:00:53.00,0:00:57.00,Default,,0000,0000,0000,,and it leads us beautifully to our next lesson
Dialogue: 0,0:00:57.00,0:01:01.00,Default,,0000,0000,0000,,when we talk about very large experiments and the normal distribution.
Dialogue: 0,0:01:01.00,0:01:06.00,Default,,0000,0000,0000,,What you should have learned and understand now is you can take very large experiments
Dialogue: 0,0:01:06.00,0:01:13.00,Default,,0000,0000,0000,,with large numbers of coin flips and compute the probability that heads comes a certain number
Dialogue: 0,0:01:13.00,9:59:59.99,Default,,0000,0000,0000,,of times using the formula that you should now fully and wholly understand.