So let's break this problem down looking at some joint probabilities.

What we know so

far is probability of success, this is our prior information, is 60%.

Probability of failure is going to be 40%.

That's some of the information that we already have.

All right, well, based on the reliability information and using the multiplication

role, we can construct what's the probability of saying that we should

launch the movie, that it's a go decision, and the movie is going to be successful.

Well, we're going to use the product rule.

What's the probability that they said go, given that movies were successful?

That reliability information was 90%.

We had that previously.

The prior information, 60% chance of probability.

Multiply them together, that's going to give me the 54%.

Similar approach for probability of them recommending we

launch the movie and it being a failure.

Well, of those movies that were failures,

they said that the movie should be launched 20% of the time.

Overall, probability of a failure is 40%, joint probability is 8%.

All right, now we can take the same approach to fill in

the last two cells on this grid.

Now, if I were to add up the probability, going across the row,

I've got 54%, I've got 8%.

What's the probability of saying that I should go ahead and launch the movie?

It's going to be 62%.

Now we can actually go and

fill out the remainder of this table using addition rules, right.

So my probability of success is 60%.

My probability of success and go was 54%.

So what remains, well, this is only going to be a 6% probability remaining.

This one's going to be a 32% probability, again 40%,

I've already accounted for 8%, that's where that's coming from.

So the probability of the no-go is going to be 38%, and

that's coming from just adding from across this row, the 6% and the 32%.

Or saying, well if I don't launch the movie 1 minus the 62%,

I'm recommending don't launch with 38%.

So let's first focus on that 62 and 38% and

fill that in on the table, then we'll come back for the rest.

All right, so the information that we've filed in so far,

based on the company saying go verses no-go, how frequently does that happen?

The go recommendation comes 60% of the time,

the no-go recommendation comes 38% of the time.

Now we're going to move down to calculating once we've moved down each of

this paths, the success and failure given the go and no-go decision.