Lance the Wizard has been informed that tomorrow there will be a 45% chance of encountering the evil Myrmidons and a 20% chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a 12% chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog ?
A)0.45
B) 0.36
C) 0.46
D) 0.52
E) 0.47

Question

Lance the Wizard has been informed that tomorrow there will be a 45% chance of encountering the evil Myrmidons and a 20% chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a 12% chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog  ?
A)0.45
B) 0.36
C) 0.46
D) 0.52
E) 0.47

Quizplus · Accepted Answer

To find the probability of encountering neither the Myrmidons nor the Balrog, we first calculate the probability of encountering at least one of them and then subtract this from 1. The formula to find the probability of A or B happening (where A and B are two events) is P(A or B) = P(A) + P(B) - P(A and B). Here, P(A) = 0.45 (Myrmidons), P(B) = 0.20 (Balrog), and P(A and B) = 0.12 (both). So, P(A or B) = 0.45 + 0.20 - 0.12 = 0.53. Therefore, the probability of encountering neither is 1 - 0.53 = 0.47.

Lance the Wizard Has Been Informed That Tomorrow There Will