2. Given events A and B (a) let C be the event that A will occur and B will not

Question

2. Given events A and B (a) let C be the event that A will occur and B will not occur. Express C in terms of A andd B. Let D be the event that B will occur and A will not occur. Express D in terms of A and B (b) let E be the event that exactly one of the events A or B will occur. Express E in terms (c) Use the result in (a) to find a formula for the probability of E in terms of the quantities (d) Compare the resulting formula with the formula for P(F), where F is the event that at of A and B. P(A), P(B) and P(An B) least one of the events A or B will occur

Explanation / Answer

a) C = A B'

D = A' B

b) E = (A B') + (A' B)

c) P(E) = P(A B') + P(A' B) = P(A) - P(A B) + P(B) - P(A B) = P(A) + P(B) - 2P(A B)

d) P(F) = P(A) + P(B) - P(A B) = P(E) + P(A B)

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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