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Chapter 7: Problem 88

Swords and Sorcery Lance the Wizard has been informed that tomorrow there will be a \(50 \%\) 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 \(10 \%\) chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?

Short Answer

Expert verified
The probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog is \(40\%\).

Step by step solution

01

Find the Probability of Encountering either Myrmidons or Balrog (P(M 鈭� B))

To find the probability of encountering either Myrmidons or Balrog, we can use the formula: P(M 鈭� B) = P(M) + P(B) - P(M 鈭� B) Using the given probabilities: P(M 鈭� B) = 0.50 + 0.20 - 0.10 P(M 鈭� B) = 0.60 The probability of encountering either Myrmidons or Balrog is 60%.
02

Find the Probability of NOT Encountering Either Enemy (P(卢(M 鈭� B)))

To find the probability of NOT encountering either Myrmidons or Balrog, we'll subtract the probability of encountering at least one of them (P(M 鈭� B)) from 100%. P(卢(M 鈭� B)) = 1 - P(M 鈭� B) P(卢(M 鈭� B)) = 1 - 0.60 P(卢(M 鈭� B)) = 0.40 The probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog is 40%.

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