5)
(a)
(b)
(c)
(d)
6)
Infected | healthy | Total | |
tested positive | 40 | 5 | 45 |
tested negative | 10 | 45 | 55 |
Total | 50 | 50 | 100 |
a)
b)
c)
d)
Hence E and F are not independent
5. Suppose E, F, and G are three disjoint events where P(E)- .15, P(F)- .25, and...
[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.
QUESTIONS Let E and F be two events of an experiment, and suppose Pr(E)=0.3. Pr{f}=0.2 and Pr(ENF)=0.15. Find each of the following probabil Round answers to deal places where needed Pr EUF) PrE) Pr{E' F) Pr{EF)
Consider a small town that has a population of 1,000 people. It is known that in this town, 10 people are infected with a rare disease. The remaining 990 people are NOT infected with the disease. This data is known with certainty. Recently, The FDA (Food and Drug administration) developed a test that determines if a person is infected with this disease. However, as with most test of this nature, it is not foolproof proof as there are a certain...
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
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).
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
question1: If events E, F & G are mutually independent, and P(E) = P(F) = P(G) = .3, then P(EF' | G) = a) .16 b) .18 c) .20 d) .21 e) .24 question2: A multiple choice history exam contains 5 choices per question. Sally knows 90% of the material that the exam covers. When she doesn’t know the answer to a question, she guesses. Determine the probability that Sally knew the answer to problem #17, given that she answered...
You are given the following information about events A, B, and C P(A)0.35, P (B)-0.3, P(C) 0.51 Events A and B are independent. The probability of at least two of these events occurring is 0.27. The probability of at exactly two of these events occurring is 0.2 Find P(4jc) 0.3698 0.3489 0.3384 0.3279 0.3593 It is known that 2.6% of the population has a certain disease. A new test is developed to screen for the disease. A study has shown...
Note: This is using Bayesian statistics (a) Suppose that in a population, the probability of having a rare disease is 1 in 1000. We use θ to denote the true probability of having the disease. A diagnostic test for this disease has a sensitivity of 99% and a specificity of 95%. A randomly selected person from the population is administered the test and the test and it comes up positive (the test suggests that the person has the disease). What...
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.