that we have 95 aircrafts, spacecrafts, that were hit by a laser beam,

out of 195 total, that we have no deficit.

So 95 divided by 195 would give us this 49%.

Similarly we can try to answer the second question.

What's the joint probability of surviving the asteroids and

avoiding the laser beams?

Well, now we have to calculate the probability of two events.

Actually the probability of surviving the asteroids and

the probability of avoiding the laser beams.

So the favorable cases that we would have to divide by the total cases in this

case are those in which a spacecraft survives the asteroids,

and those in which they avoid the laser beam.

So if you go to the contingency table,

you would be able to see that this number is 37.

So if we divide 37, which are our favorable cases,

by the total number of cases, 195, this yields the probability

of surviving and avoiding the laser beam, which is 19%.

Now we can increase a little bit the difficulty of the question and

ask, given that the spacecraft is hit by a laser beam,

what's the probability of being alive after crossing the asteroid field?

Well, in this case we know for sure that the spacecraft is hit by laser beam.

So, this reduces the relevant state space that we can, or

that we have to use to make our calculation.

In this case it's the relevant space case is reduced to 95 cases.

Actually, those in which the aircraft, the spacecraft, is for

sure hit by the laser beam.

Then we take at favorable cases again

which is those in which the spacecraft survive.

And we see it's only two in the contingency table, so if we divide two by

95, we get the probability that we're looking for which is 2.1%.

Now we can scroll down a little bit and

try to answer our last question which is also very similar to the previous one.

Now, given that the space craft escapes the asteroid field,

what's the probability of having been hit by a laser beam?

So, now we see again that the relevant state space gets updated again

to the cases in which the space craft survives the asteroids,

the crossing of the asteroid field, which is 39 cases.

We would then take our favorable cases, which would be those in which

the spacecraft manages to escape the asteroid field, which are only 2,

and then divide it by our relevant state space, 39.

This will give a probability of 5.1%.