Set Theory and Conditional Probability Problem #1 : (10pts) If P(A) 0.3 and P(B)0.2 and P(A...
SHOW STEP BY STEP ON A PAPER PLEASE WITH A CLEAR HANDWRITING. The following table summarizes the number of deceased beetles under autolysis (the destruction of a cell after its death by the action of its own enzymes) and putrefaction (decomposition of organic matter, especially protein, by microorganisms, resulting in production of foul-smelling matter): Autolysis High 14 30 Low 47 High Low Putrefaction (a) If the autolysis of a sample is high, what is the probability that the putrefaction is...
4. IfP(A) 0.3, P(B) 0.2, and P(An B) 0., determine the following probabilities: (b) P(AU B) (c) P(A'n B) (d) P(An B') (e) P[(A U B)] (f) P(A'U B) 5. The following table summarizes the analysis of samples of galvanized steel for coating weight and surface roughness: Coating Weight High High Low Low 16 34 Surface 12 Roughness If the coating weight of a sample is high, what is the probability that the surface roughness is high? If the surface...
The events X and Yare mutually exclusive. Suppose P(X) 0.07 and P(Y) 0.05 (1) What is the probability of either X or Y occurring? (Round your answer to 2 decimal places.) Probability (2) What is the probability that neither X nor Y will happen? (Round your answer to 2 decimal places.) Probability
Problem 3: If P(A) 0.2, P(B) 0.1, and P(A or B) PIA U B) 0.28, then (a) (2.5 points) find the P(A and B). That is, find P(AnB). (b) (2 points) clearly explain whether the events A, B are mutually exclusive (disjoint). (c) (2 points) clearly explain whether the events A, B are independent based on probability
Problem 1. A biased coin with probability plandin with a Heads is lipped 4 times. (a) Define the basic random variables and give the sample space and assign probabilities to the outcomes. (b) Let X be the total number of Heads in the four flips Draw a Venn diagrain showing the five events X = ii 0,1,2,3,4 as well as the sample space and the outcomes. Is X a random variable? c) Are the events X 1 and X 2...
1. Let (S;F;P) be a probability space with A 2 F and B 2 F such that P(A) = 0:3 and P(B) = 0:4. Find the following probabilities under the specified conditions. Note that I don’t expect you to have to show much work in answering this question. (a) either A or B occurs if A and B are mutually exclusive (b) either A or B occurs if A and B are statistically independent (c) either A or B occurs...
I want the solution for this. Stat 352 Homework Set 2 Fall 2019: Conditional Probability and Independence Deadline: Monday November 11, 2019 (1) In throwing two dice with the sample space Define the following events on : = {(x,y):x, y = 1,2,3,4,5,6). A = {sum less than 4) = {(x, y): x + y < 4, x, y = 1,2,3,4,5,6) B = {first number is 1) = {(x,y): x = 1, y = 1,2,3,4,5,6) C = {sum of number is...
1. If AA and BB are two mutually exclusive events with P(A)=0.3 and P(B)=0.6, find the following probabilities: a) P(A^c)= b) P(B^c)= c) P((A∪B)^c)= d) P(A∩B^c)= 2. An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 104 students in the school. There are 43 in the Spanish class, 34 in the French class, and 24 in the German class. There are 17 students...
1) Events A, B, C, and D are mutually exclusive and collectively exhaustive. If P(A or B) = .44. Circle all of the following that are possible? a) P(C or D) > .56 b) P(C and D) = .56 c) P(A and D) = 0 d) P(A) = .5 2) You have 10 members of a team. How many ways could you pick 3 captains (order does not matter)? a) 720 b) 30 c) 120 ...
Conditional Probability Problem 1) A foundry has 3 different production lines and wants to evaluate the performance of each line. The performance of each line is given below Percent of all parts that Percent of all parts that come from each line and Line X Line Y Line Z TOTAL come from each line 44% 36% 20% 100% are defective 3% 4% 1% 19% Parts from all 3 lines merge into a single conveyor to take them to inspection. Consider...