Respuesta :
Answer:
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:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that he only encounter evil Myrmidons and [tex]A \cap B[/tex] is the probability that he encounters both.
By the same logic, we also have:
[tex]B = b + (A \cap B)[/tex]
The sum of all the probabilities is decimal 1, so:
[tex]a + b + (A \cap B) + C = 1[/tex]
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 [tex]A \cap B = 0.1[/tex].
30% chance of meeting up with the dreadful Balrog.
This means that [tex]B = 0.3[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]0.30 = b + 0.10[/tex]
[tex]b = 0.20[/tex]
40% chance of encountering the evil Myrmidons
This means that [tex]A = 0.4[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]0.40 = a + 10[/tex]
[tex]a = 0.30[/tex]
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:
[tex]a + b + (A \cap B) + C = 1[/tex]
[tex]0.30 + 0.20 + 0.10 + C = 1[/tex]
[tex]C = 0.40[/tex]
There is a 40% probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog.
