Lance the wizard has been informed that tomorrow there will be a 40% chance of encountering the evil myrmidons and a 30% chance of meeting up with the dreadful balrog. moreover, hugo the elf has predicted that there is a 10% chance of encountering both tomorrow. what is the probability that lance will be lucky tomorrow and encounter neither the myrmidons nor the balrog?

There is a 40% probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog.

Step-by-step explanation:

We can solve this problem using the Venn's Diagram of these probabilities.

I am going to say that:

A is the probability that he encounters evil Myrmidons.

B is the probability that he encounters dreadful Balrog.

C is the probability that he does not encounter any of them.

We have that:

In which a is the probability that he only encounter evil Myrmidons and is the probability that he encounters both.

By the same logic, we also have:

The sum of all the probabilities is decimal 1, so:

We start finding these values from the intersection of both sets:

Hugo the Elf has predicted that there is a 10% chance of encountering both tomorrow.

This means that .

30% chance of meeting up with the dreadful Balrog.

This means that

40% chance of encountering the evil Myrmidons

This means that

What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?

This probability is the value of C. So:

There is a 40% probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog.