31 – Binomial Distribution Conclusion

In this lesson, we found the probability that a coin would land on heads k times out of n flips. If the probability of heads for the coin is p, we get the following formula for the probability that the number of heads will be k. The first half is n factorial over n minus … Read more

30 – Binomial 6 Solution

And the approximate answer is 0.236. That’s the probability of exactly 9 heads out of 12 coin flips for this heavily loaded coin that mostly gives you heads. And again, the answer is 12!/12-9. This is 3! 9!. Then we have to compute the probabilities being (0.8)⁹ and 1-0.8 is 0.2³ and that is the … Read more

26 – Binomial 4 Solution

So interestingly enough, we can do the trick as before 5!/4!*1!, which is the number of outcomes at exactly 4 heads and we know that’s 5. Four heads means one tails. There’s five ways to place one tails and this one over here. The question now what’s the probability of those? Well, they have heads … Read more

25 – Binomial 4

Let’s now say for the same loaded coin, we flip that coin five times with that same load of probability over here and we care about the out of five times heads comes exactly four times. Now, I want you to compute this probability over here, It’s a completely nontrivial question. If it’s too hard, … Read more

24 – Binomial 3 Solution

So here is my truth table of these eight different outcomes. The ones that has head exactly once are this one, this one, and this one, but they’re not all equally likely. Heads, heads, heads is much more likely than say tails, tails, tails because heads has a probability of 0.8^3. This one here has … Read more

23 – Binomial 3

Now, I’m going to make it really difficult. I’m going to give you a coin–let’s call it loaded. So, the probability for heads will now be 0.8 and therefore the probability for tails is 0.2. To make it easier, assume only a 3 coin flips and ask the probability of heads coming up exactly once. … Read more

20 – Binomial 1 Solution

Now, we know from our previous consideration that there are five ways in which the number of heads could be one. 5!/4! 1! happens to be 5. We also know that there are 32 possible outcomes. It is 2⁵=32 outcomes. This is the size of a truth table. So, 5 out of 32 outcomes has … Read more