Reduced collateral damage.

We put in the value of n, and we call it again.

And with this means, with the positive test result, our chance of cancer increased from 0.1 to 0.16.

The inner loop of the summation now has only 3 terms rather than 5 terms.

However, if I now divide, that is, I normalize those non normalized probabilities over here by this factor over here,

Let's use the Laplacian smoother with K 1 to calculate the few interesting probabilities

To change this example even further.

And what's interesting is, the four out of six heads, it kind of decreased the probability that we got a fair coin.

This is just the theorem of total probability or forward propagation rule applied to this case over here, so nothing really new.

So we divide by the total weight of all particles, and we get out those probabilities over here.

Let me quickly go over the proof.

We now apply Bayes rule.

So let's look at this, let's look at a population where the probability of success we'll define success as 1 as having a probability of p, and the probability of failure, the probability of failure is 1 minus p.

The probability of any random variable Y can be written as probability of Y given that some other random variable X assumes value i times probability of X equals i, sums over all possible outcomes i for the (inaudible) variable X.

The probability of observing X and Y depends on what state the hidden markov model is in.

For A, it's 0.1 for X and 0.9 for Y.

Any probability of X2 being in a certain state must have come from another state, X1, and then transitioned into X2, so we sum over all of those and we get the posterior probability of X2.

Altitude

You learned about probability of an event, such as the outcome of a coin flip.

But it might've been we didn't move, in which case you just use the probability of that specific cell multiplied by the probability of staying.

And we could do the same thing on the other side. What if O had to go first?

Let's now go to the extreme, and this is a challenging probability question.

So therefore the answer to this question would be 0.5, or half.

In the second question we apply total probability.

For example, p might be 0.5.

I want to introduce the, the idea of probability here just, just in a very, very basic way.

We asked them to estimate their likelihood of experiencing different terrible events in their lives.

You remember that we cared about a grid cell xi, and we asked what is the chance of being in xi after robot motion?

Here we're given a marchov chain between A and B, with the transition of A to itself is 0.9 with 0.1 chances transitions to B.

So let's say I want to figure out the probability I'm going to flip a coin eight times and it's a fair coin.

Let's say, let's roll a dice.

And this expression equals 0.6080 and so the probability that we have the same coin is simply the probability that we both have type 1 or fair coins, plus the probability of my having coin 2 times the probability of your having coin 2.

You might say OK, that's the probably of getting exactly 1 times the probability of getting 2 out of 3 plus the probability of getting 3 out of 3.

On the second state we know that the probability of R is 0.6 and therefore, the probability of sun is 0.4, and we compute the probability of rain on day 2 using total probability.

Decreases the components reference counter.

least maybe it doesn't make intuitive sense just yet, but I showed you that the probability of a and b is equal to the probability of a given b times the probability of b.

The motions don't move at all, move right, move down, move down, and move right again.

But we don't know for sure that they're exclusive events.

And we know that our variance is essentially the probability of success times the probability of failure.

Some have 0.13, but the one over here has a probability of 0.533.

As is easily seen, the 0.5 falls out, so we get 0.1 over 0.9 over a ninth, which is the answer for the first question.

This form is easily transformed into this expression over here, the probability of the message given spam times the prior probability of spam over the normalizer over here.

So that tells us the probability of a given b times the probability of b, is equal to the probability of b given a, times the probability of a.

This can be resolved as follows.

And it makes much more sense to talk about the probability or random variable equaling a value, or the probability that it is less than or greater than something or the probability that is has some property