Is it possible to have an assignment of probabilities such that P(A) 1/2, P(AnB)- 1/3 and...
Let A and B be events with probabilities P(A)-3/4 and P(B)-1/3 (a) Show that 12 3' (b) Let P(AnB) - find PA n Bc).
Match the rules to their correct notation: >P(AnB) P(A) (BIA) 1. Addition Rule 2. Multiplication Rule P(A) Independent events Multiplication Rule - Dependent events 3. P(AnB)P(A) P(B) PAUB)PA)P(B)(AnB) 4. Conditional Probability
Use P(A UBU)PCA) +P(B) + P(AnB)-This gives (-1)k+1 ㄧㄨㄧㄧ-)+ k=1 1--~ 0.632121 k! Homework Your assignment is to show how we get these last two equalities.
(1) If A and B are two events suchthat PA)1.P(B) -and P(AnB) -.Determine the following: 3 i) P(AU B) v) PCA'U B) ii) P(A'n B) vi) P(A'- B) iv) P(AnB') viii) P(A'-B')
8. Let P(A) P(B) - 1/3 and P(AnB) 1/10. Find the following: (b) P(AUB') () P(Bn A (d) PA UB)
1 Let A and B be independent events with P(A) and P(B) = FICE Find P(ANB) and P(AUB). 8 P(ANB) = P(AUB) =
If P(A)=0.7 ,P(B') = 0.6 and P(AUB)=0.9, then P(ANB) = ? 2. If P(A)=0-7, P(B)=0.6 and P(AUB) - 0.9, then plAl(AUB)) = ? 3 Afair dice is rolled, probability of getting a number & such that 1 <x<8 is = ?
In each of the situations, choose whether or not the given assignment of probabilities to individual outcomes is legitimate. Remember, a legitimate model need not be a practically reasonable model. If the assignment is not legitimate, choose the correct reason for your answer. (a) Roll a six‑sided die and record the count of spots on the up‑face: ?(1)=0,?(2)=1/6,?(3)=1/3,?(4)=1/3,?(5)=1/6,?(6)=0P(1)=0,P(2)=1/6,P(3)=1/3,P(4)=1/3,P(5)=1/6,P(6)=0 . This is not a legitimate model because the sum of the probabilities does not equal 11 . This is not a...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
Problem 3. Show the formula P((An B)U(A n B))- P(A) +P(B)-2P(AnB), which givgs the probability that exactly one of the events A and B will occur. [Compare with the formula P(AU B) P(A) P(B) - P(AnB), which gives the probability that at least one of the events A and B will occur.]