QUESTIONS Let E and F be two events of an experiment, and suppose Pr(E)=0.3. Pr{f}=0.2 and...
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)
[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.
F) - 0.2. Compute the values below. Let E and F be two events of an experiment with sample space S. Suppose P(E) - 0.5, PF) - 0.4, and P( E (a) P(EUA) (b) PCE) (c) PFC) (d) PRE-
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]?
Let E and F be two events of an experiment with sample space S. Suppose P(E)= 0.4, P(F)=0.3, P(E U F) =0.5, Find P(F|E) and determine if the two events are independent. A) P(F|E)= 3/4, E and F are independent. B) P(F|E)= 3/4, E and F are not independent. C) P(F|E)=1/2 , E and F are independent. D) P(F|E)= 1/2, E and F are not independent.
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...
if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3
Exercise 1. The base composition of a certain microbial genome is pc - - 0.3 and pA -pr -0.2. We are interested in 2-words where the letters (a) Present these 16 probabilities in a table. (Do your 16 numbers sum to (b) Purine bases are defined by R- A, G} and pyrimidine bases by Y - C,T are assumed to be independent. There are 4 x 4 16 2-words. 1.0? Let E be the event that the first letter is...
Assume that events (E, F) are disjoint, and their probabilities are specified as (here p. An experiment is repeated until either E or F will occur Find the probability that E will occur before F Hint Introduce a random variable, N, which is the first occurrence of EUF. Then express the probability that E occurs before F, given that EUF occurs at the time N and use the formula where A is the desired event
Problem #9: Let E and F be events whose probabilities are given in each case below. In which cases are E and F independent? (i) Pr(E) = 0.9, Pr(F) = 0.8 and Pr(FUE) = 0.99. (ii) Pr(E) = 0.4, Pr(F) = 0.5 and Pr(FUE) = 0.69. (iii) Pr(E) = 0.3, Pr(F) = 0.1 and Pr(FUE) = 0.37.