Use P(A UBU)PCA) +P(B) + P(AnB)-This gives (-1)k+1 ㄧㄨㄧㄧ-)+ k=1 1--~ 0.632121 k! Homework Your assignment...
Use P(A U B U gives ) = P(A) + P(B) + . . .-P(A n B)-... This 1m k+1 nn-1 に! lim 一= 1 k! ~ 0.632121 に! Your assignment is to show how we get these last two equalities.
V n balls are numbered one through n; draw them (without replacement); what is the probability that at least one ball will be drawn with its number equal to the number of balls drawn? As n -oo what is the probability? Use P(A U BU...)P(A) +P(B) +-P(AnB)- This gives -1)1 n n-1 = 1 ~-~ 0.632121 kl Your assignment is to show how we get these last two equalities
2.4. Prove AN(BUC) -An B)U(ANC) P(AUB) = PCA)+PCB)- P(ANB)
By only use these axioms to solves the following two
questions. Thank you.
(AUB)A nB (AnB) AUB 0 EPCA)E P(S)=I PCAUB) P(A) P(B)-PIAne) P(AIB) # ot times A and Boccur #ot times B ocuuts P(ADP(ANB) PCB) P/AB)P(BIA)P(A) P(B) Taew ledr- Using notin The defa P (A I8), The 3 axioms, and T "lews" Teem we have discussed (e. more 1 Show TR P(ALB ) PLACIB) uw-leuti9-2AsSsume AnBUc) (AnB) U (ANC) Mew show Tt Pl(AU B)UC) PIAT+ PCB) Pc) PCANB) PIANC)-...
Is it possible to have an assignment of probabilities such that P(A) 1/2, P(AnB)- 1/3 and P(B) 1/4?
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.]
Show proof of P(AUBUC) - P(A)+P(B) +PCC) - P(ANB) -P(BnC)-Planc) + P(AMBAC) use D to replace a use thm. P(AUB) = P(A)*P(B)- P(ANB)
(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')
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) =
Use the given information to find the indicated probability. P(A) = 0.1, P(B) = 0.8, PCA n B) = 0.05. Find P(A UB). P(A U B) =