Let P(E)= 0.37, P(EF)= 0.19, and P(EF^c)= 0.89. Find P(F|E^C).
P(E)=0.37
P(E)+P(F)=1
P(F)=1-0.37=0.63
Let P(E) = 0.28, P(EF) = 0.13, and P(EFc) = 0.82. Find P(F|Ec)
Let P(E) = 0.28, P(EF) = 0.17, and P(EFc) = 0.88. Find P(F|Ec). ) 0.6071 b) 0.1667 c) 0.2361 d) 0.5862 e) 0.4286 f) None of the above.
Given P(E or F) = 0.89, P(F) = 0.44, and P(E and F) = 0.04, what is P(E)?
10. Prove that P(E UFUG)P(E) P(F) + 2P(EFG). 11. If P(E)9 and P(F).8, show that P(EF .7 In general, prove Bonferroni's inequality, namely, P(EF) 2 P(E) + P(F)-1 13. Prove that P(EF*)= P(E)-P(EF).
24) If events E, F & G are mutually independent, and P(E)P(F) P(G).3, then P(EF I G) a).16 b).18 c).20 d).21 e).24
Let E= 020 ool [800] F-[ ] compute (EF) using E' and fit suppose EFX: [1] find the matrix X
5. Suppose E, F, and G are three disjoint events where P(E)- .15, P(F)- .25, and P(G).60. Find the following: (a) P(F or G) (b) P(Ec) (c) P((E or F)c) (d) P(FnG) 6. A new diagnostic test for a disease is studied. It is known whether or not these 100 individuals have the disease and the diagnostic test is administered. The results are as follows infectedhealthy tested positive tested negative 40 10 45 Let E-randomly selected person is infected and...
Let E and F be events for which P(E) = .5, P(F)= .4, and P(E F) = .2 a) are E and F mutually exclusive or independent? (justify mathematically) b) Find P(E F) c) Find P(F') d) Find P(F l E) e) Find P(E' F) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. Consider a statistical experiment E: (, F,P) and an event A . Note: A EF. a. Use the axioms of probability to show that P(A) 1-P(A). b. Repeat (a) using the definition of the σ-field. 2. Consider a statistical experiment E: (, F,P) in which a fair coin is flipped successively until the same face is observed on successive flips. Let A = {x: x = 3, 4, 5, . . .); that is, A is the event that...
Let P(E) = 0.28, P(E∩F) = 0.17, and P(E U Fc) = 0.88. Find P(F|Ec).