Suppose that in a battle, the probability that Captain America throws his shield

Question

Suppose that in a battle, the probability that Captain America throws his shield is 0.8. Assume further that the probability that the Avengers win the battle if Captain America throw his shield is 9.0, and that the probability that the Avengers win the battle if Caption America does not throw his shield is 0.7. Are the events A = the Avengers win the battle and C = Captain America throws his shield independent? Provide a justification for your answer. What is the probability that the Avengers win the battle? If the Avengers win the battle, what is the probability that Captain America threw his shield?

Explanation / Answer

3. P(C) = 0.8

P(A | C) = 0.9

P(A | C' ) = 0.7

a. P(A) = P(A|C)*P(C) + P(A | C')*P(C')

= 0.9*0.8 + 0.7*(1-0.8)

= 0.86

P(A and C) = P(A|C)*P(C) = 0.9*0.8 = 0.72

P(A)*P(C) = 0.86*0.8 = 0.688, which is not equal to P(A and C).

Hence A and C are not independent.

b. P(Avengers win) = P(A) = P(A|C)*P(C) + P(A | C')*P(C')

= 0.9*0.8 + 0.7*(1-0.8)

= 0.86

c. P(C | A) = P( A | C)*P(C) / P(A) = 0.9*0.8/0.86 = 0.8372

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.