A random experiment has a sample space {m,t,b,x,z,r}{m,t,b,x,z,r}. The probability of each outcomes are given as {0.1,0.05+3a,0.1+a,0.2,0.3,0.05}{0.1,0.05+3a,0.1+a,0.2,0.3,0.05}. The following events are established for this experiment: A={m,t,b}A={m,t,b}, B={t,x,z}B={t,x,z}, C={z,r}C={z,r} and D={m,b,r}D={m,b,r}.  i). Determine the value of aa. ii). Enumerate the outcomes for (A∪B)∩(C∪D)(A∪B)∩(C∪D) and find its probability. iii). Enumerate the outcomes for (A∪C)∩(B∪D)(A∪C)∩(B∪D) and find its probability.

Q: Of a group of undergraduates, 5 are studying chemistry, 3 physics and 2 statistics. If 3 students…

A:

Q: A box holds 3 red and 5 blue marbles. If 2 marbles are to be drawn at random without replacement and…

A: Given, Red Marbles = 3 Blue Marbles = 5 Total Marbles = 8 Let X denotes the number of red marbles

Q: Illustration 16.63. The products of three factories producing radio valves are know to be 2%, 3% and…

A:

Q: Balls are labelled 2, 3, 5, 6 and 8 then are placed in a raffle box. Two balls are chosen without…

A:

Q: It is claimed that 20% of the people in a particular region have an infection. Suppose that ten…

A: Given: n=10, p=0.20.

Q: Let A and B be any two events defined on sample space omega.  Suppose that P(A) =.4, P(B) = .5, and…

A: The given probabilities are:P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1.

Q: What is the probability of finding exactly 5 green M&Ms in any one given bag?

A: Given: n= 40 P( green) = 0.15

Q: Suppose a random excitement has a sample space of {a, b, c, d, e}. The probabilities of ‘a’ , ‘b’ ,…

A: The sample space is given as follows:The probabilities of the elements are given as follows:Element…

Q: each generation be composed of four individuals, x1, x2, x3, and x4. At a given generation, the…

A: The fitness function probability is given by: pi=fi∑i=14fi Therefore:…

Q: Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes…

A: Given: The possible values X can take is {-5,-1}. The probability distribution function is obtained…

Q: A probability experiment is conducted in which the sample spce of the experiment is S =…

A: FOR ANY QUERIES, PING ME     HAPPY LEARNING

Q: Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes…

A:

Q: A foreign shipment of 5 foreign cars contains 2 that have light paint stains. Suppose an agency…

A: A random variable is an outcome of a random experiment. Sometimes the outcomes of a random…

Q: Assume that a random variable X is defined to be -4 if the result is a 1,5 if the result is a 2 or…

A: Given that the variable X is defined to be -4 if the result is a 1, X takes 5 if the result is a 2…

Q: In a university class of 200 students, where 60% are females and 40% are males, what is the…

A: Answer:   We have a university class of 200 students, 60% female and 40% male. This means we have…

Q: An experiment is performed where a 6-sided die is rolled and then a coin is flipped. The possible…

A: The objective of this question is to identify the sample space for an experiment where a 6-sided die…

Q: Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes…

A: Given information- We have given that the genders of the three children of a certain family are soon…

Q: A probability experiment is conducted in which the sample space of the experiment is S =…

A: Given:Total sample space S= {7,8,9,10,11,12,13,14,15,16,17,18}=n(S)=12Event F= {9,10,11,12,13} =…

Q: Let A and B be two events in a sample space S. Suppose P(A) = 0.5, P(B) 0.3, and P(A n B) = 0.2.…

A:

Q: A foreign shipment of 5 foreign cars contains 2 that have light paint stains. Suppose an agency…

A: In statistics, the population refers to the complete set of objects/individuals over which the study…

Q: When leaving a certain subway station a person can exit through any one of three gates, and any…

A: Given When leaving a certain subway station a person can exit through any one of three gates, and…

Q: A committee of 4 is to be randomly selected from 8 women and 10 men. What is the probability of…

A: We want to find probability of having three men on the committee.

Q: A probability experiment is conducted in which the sample space of the experiment is S =…

A: Step 1: State the given sets: S={3,4,5,6,7,8,9,10,11,12,13,14}F={6,7,8,9,10}G={10,11,12,13} Step 2:…

Q: Give an example of two different random variables which have the same probability distribution (and…

A: 1) Considering a 6 face fair die  Let random variable X represents the outcome we get when we roll…

Q: fair dice is rolled. If the outcomes are 1,2,3 or 4, a fair coin is flipped once. If the outcomes…

A: Fair dice rolled :  outcomes 1,2,3,4 Fair coin : outcomes 5,6 Amount of information for outcomes =?…

Q: If A,B are two independent event in a sample space , if P(A) = 0.7,P(B) =0.6. Find PAU B) Select…

A: According to the provided information, we have A and B are two independent…

Q: Suppose our population is made up of the 12 individuals whose monthly INCOME: 40, 41, 42, 43, 44,…

A: The given variable is Income. Let us denote by X.The given values of X are 40, 41, 42, 43, 44, 45,…

Q: Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting…

A: Here given , A probability experiment is conducted in which the sample space of the experiment is…

Q: Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes…

A: If the probability of getting selected for each outcome is equal then such outcomes can be termed as…