Given P(E) = .5 P(F) = .5 P(E AND F) = .25
Are E and F Independent?
Are E and F Mutually Exclusive?
P(E AND F) = 0.25
P(E) * P(F) = 0.5*0.5 = 0.25
Since P(E AND F) = P(E) *P(F) , E AND F are independent
Here, P(E and F) is not equal to 0
So, not mutually exclusive
1. find p(e/F) given that p(F) = .88 and p(F) = .82 e and f are independent events. 2. fine p(E/F) give. that p(E) = 0.0 and p(F) = .6 e and f are mutually exclusive 1. find P(E/F) given that P(E)= .88 P(F)= .82
Suppose that E, F, and G are events with P(E) = 8/25 , P(F) = 11/50 , P(G) = 23/100 , E and F are mutually exclusive, E and G are independent, and P(F | G) = 20/23 . Find P(E ∪ F ∪ G).
3.2 Independent and Mutually Exclusive Events 40. E and Fare mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E|F)41. J and K are independent events. P(J|K) = 0.3. Find P(J) 42. U and V are mutually exclusive events. P(U) = 0.26: P(V) = 0.37. Find:a. P(U AND V) =a. P(U|V) =a. P(U OR V) =43. Q and Rare independent events P(Q) = 0.4 and P(Q AND R) = 0.1. Find P(R)
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
Complete each probability rule. If E and F are mutually exclusive events then P(E UF)- P(E)+PF) P(E) P(E I F) PE) + P(F) # 1 P(E)- 1- P(E) 1-P(E) If E and F are mutually exclusive events then P(E)+ P(F) If E and F are independent events, then P(E IF) number of outcomes in E number of outcomes in sample spaceE)PF
Suppose P (E) = 3/7 and P (F ) = 2/7 . Each of the following answers should be given as 77 a single fraction. (a) [6 pts] If E and F are independent events, find P (E ∩ F ). (b) [6 pts] If E and F are mutually exclusive events, find P (E ∪ F ). (Do not assume independence for this part.)
E and F are mutually exclusive. P(E) = 0.2, P(F) = 0.8 Find P(E È F)
Suppose that P(E)=0.36 P(F)=0.12 and E and F are mutually exclusive. What is P(E and F) Upper P left parenthesis Upper E or Upper F right parenthesisP(E or F)?
3.) Given that P(A) = .5, P(B) = .4, and P(A and B) = 2, Find each of the following. A venn diagram may help) a. P(A or B) b. P(B) c. P(AB) d. P(BA) 4.) Event E and F have probabilities P(E) = .5,P(F) = 4, and P(E and F) = 2 a. Are E and F mutually exclusive? Explain your answer. b. Are E and Findependent? Explain your answer
e and E and P events associated with S. Suppose that Pr(E)-0.5, Pr(F) -0.4 (a) If E and F are independent, calculate: i. Pr(EnF) ii. Pr(EUF) iii. Pr(El) iv. Pr(FIE) (b) If E and F are mutually exclusive, calculate: i. Pr(ENF) ii. Pr(EUF) iii. Pr(E|F) iv. Pr(FIE)