independent events A and B in a sample space S, but assume that Pr[A]=0.3 and Pr[B]=0.15. Compute the following conditional probabilities: (1) Pr[A|B]= equation editorEquation Editor (2) Pr[B|A]= equation editorEquation Editor
Since P(A) and P(B) are independent
a) Pr[A | B] = Pr[A] = 0.30
b) Pr[B | A] = Pr[B] = 0.15
independent events A and B in a sample space S, but assume that Pr[A]=0.3 and Pr[B]=0.15....
E, F, and G in a sample space S. Assume that Pr[E]=0.5, Pr[F]=0.45, Pr[G]=0.55, Pr[E∩F]=0.3, Pr[E∩G]=0.3,and Pr[F∩G]=0.25. Find the following probabilities Pr[E∪F] = Pr[F′∩G]= Pr[E′∩G′]=
A and B of a sample space S, but assume that Pr[A]=0.2 and Pr[B]=0.6. Find Pr[A∪B] under each of the following conditions: (1) If A⊂B, then Pr[A∪B]= (2) If A∩B=∅, then Pr[A∪B]= (3) If A∩B′=∅, then Pr[A∪B]=
F and G are disjoint events in sample space S . If Pr(F)=0.35, and Pr(G)=0.4, find each of the following probabilities. What is Pr(F∩G)? What is Pr(F′∩G′)? What is Pr(G′|F)? What is Pr(G|F)?
J,K, and L are events in sample space S. Pr(J)=0.3 Pr(K)=0.34 Pr(L)=0.43 Pr(J intersect K)=0.16 Pr(J' intersect L')=0.44 Pr(K' intersect L)=0.24 What is Pr(L|J)? What is Pr(K|L')?
[15] 4. Let E and F be events of sample space S. Let P(E) = 0.3, P(F) = 0.6 and the P(EUF) = 0.7. a) Fill in all probabilities in the Venn diagram shown. S b) Find P(EnF). c) Find P(ENF). d) Find the P(E|F). e) Are E and F independent events? Justify your answer.
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
Let A and B be events in the same sample space, such that Pr[A] = 2/5, Pr[B] = 3/10, and Pr[A|B] = 2/3. What is Pr[B|A]? Thank you :)
Suppose E and F are independent events. Find Pr[E′∩F] if Pr[E]=1/3 and Pr[F]=1/3 A and B are independent events. If Pr(A∩B)=0.24 and Pr[A]=0.3, what is Pr[B]?
1. Events A and B are defined on a sample space S such that P((A ∪ B) C) = 0.5 and P(A ∩ B) = 0.2.If P(A) = 0.3, what does P((A ∩ B) | (A ∪ B) C) equal?
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3. Complete the following probability table. (Round your answers to 2 decimal places.) Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities P(B1) = 0.15 P(A | B1) = 0.40 P(A ∩ B1) = P(B1 | A) = P(B2) = P(A | B2) = 0.65 P(A ∩ B2) = P(B2 |A) = P(B3) = 0.32 P(A | B3) = 0.75 P(A ∩ B3) = P(B3...