### Combinations and Subsets : Probabilities

A committee consists of 8 married couples. In how many ways can a subcommitee of 5 people be chosen so that at most one married couple belongs to the subcommittee?

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A committee consists of 8 married couples. In how many ways can a subcommitee of 5 people be chosen so that at most one married couple belongs to the subcommittee?

Fort Lost-in-the-Woods is a basic training center for new Army recruits. Upon arriving at the military post the new recruits are processed through the Induction Center that involves three steps: background information gathering, medical examination, and barracks assignment. Arriving inductees first enter the Center's Background

A secretary periodically checks to see how mnay of the three lines into the office are busy. Her findings for one week were the following: No. Lines busy Frequency 0 20 1 65 2 25 3

A student applies for two different scholarships. The probability of receiving the first scholarship is 0.3 and the probability of receiving the second is 0.4. The decisions are made independently. Find the probability the student receives exactly one scholarship. A. 0.12 B. 0.42 C. 0.46 D. 0.40

If the probability that at least one person makes an A on the final exam is 0.15, then the probability no one makes an A is: A. 0.15 B. 0.65 C. 0.85 D. 0

A computer store has 10 copies of a word processing program, 12 copies of a spreadsheet program, and 8 copies of a draw program. Three of the word processing, four of the spreadsheet and two of the draw programs are infected with a computer virus. If a program is selected at random, the probability it is infected with a virus

The sample space of an experiment is {A, B, C, D} and P(A) = 0.1, P(B) = 0.3, P(C) = 0.4, P({A, C}) = A. 0.4 B. 0.5 C. 0.6 D. 0.8

A Recent survey indicates that the average salary of all entry-level women managers in St. Paul is $56,700 with a standard deviation $7,200. What is the probability that a random sample of 50 such women will yield a mean entry-level that exceeds $58,000?

The single shot probability of kill of any weapon system (gun, missle or slingshot) is less than 1 due to the reliability factors if no other reason. Suppose the single shot probability of kill of a new defensive missle system is 0.75%, and the the probability is not considered adequate. One familiar strategy to increase the o

The ELISA test was introduced in the mid-1980s to screen blood for the presence of AIDS antibodies. When antibodies are present ELISA is positive 98% of the time; when the blood lacks the antibidies the ELISA is positive 7% of the time. Assuming that 1% of the population has AIDS antibodiesin their blood, what is the probabili

According to an automobile manufacturer, the company uses 3,000 lock-and-key combinations on it's vehicles. Suppose that you find a key for one of those cars. a) What is the expected number of vehicles that you would have to check to find one that fits your key? b) What is the probability that you would have to check

Alex and Mark are playing a game. The goal is to get to 100. The first player picks a whole number from 1 to 10, inclusive, and then the second player picks a whole number from 1 to 10 and adds it to the score so far. The first player repeats this move. They continue this way. The player who makes the score exactly 100 wins.

In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices? Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually. A class consists of 15 students.

All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors & 62% are business majors. If there are 200 students, how many of them are majoring in both psychology & business?

The numbers 1 through 9 are written individually on nine cards. Choose three cards from the nine, letting x, y, and z denote the numbers of the cards arranged in increasing order. A. There are ____ ____ such as x, y, and z combinations. B. The probability of having x, y, and z all even is . C. The probability of ha

A carton of 30 lightbulbs includes 5 defective ones. If 4 light bulbs are drawn at random (without replacement), what is the probability that; (a) 2 of the selected light bulbs are defective. (b) Not all the selected light bulbs are defective.

A lot consisting of 100 fuses is inspected by the following procedure: 5 fuses are selected randomly, and if all 5 "blow" at the specified amperage, the lot is accepted. Suppose that the lot contains 10 defective fuses. Find the probabily of accepting the lot. HINT: Let X ba a r.v. equil to the number of defective fuses in

The Question is: Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3. If you are equally likely to choose either company for your first car, what is the probability that

The Question is: In the game of bridge, each of 4 players is dealt 13 cards. If a certain player has no aces, find the probability that that person's partner has: a.)no aces b.)at least 2

In class we are learning about conditional probability and independence. The question is: On a multiple-choice test you know the answers to 70% of the question (and get them right), and for the remaining 30% you choose randomly among the 5 answers. What percent of the answers should you expect to get right?

Consider a structure in which the minimal path sets are {1, 2, 3} and {3, 4, 5} a. What are the minimal cut sets? b. If the component lifetimes are independent uniform (0,1) random variables, determine the probability that the system life will be less than ½ .

Please see attached file. --- Let A, B be mutually exclusive events and P(A) = 0.4, P(B) = 0.3 Find... ---

4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. A. Why will some numbers come up more frequently than others? B. Each die has six sides numbered from 1 to 6. How many possible ways can

5. (Sudden death) The NHL has another season-long strike, but the owners and players reach an agreement in June which leaves time for a highly abbreviated season. They decide that fans want to see the Stanley Cup decided, and so they play only a sudden-death version of the seventh game of the final round of the playoffs. Her

Each individual letter of the word "pfeffernuesse" is placed on a piece of paper, and all 13 pieces of paper are placed in a hat. Three letters are selected at random from the hat. Find the probability of selecting each of the following. a) with replacement b) without replacement 1) Pulling T

A committee of four is to be randomly selected from a group of seven teachers and eight students. Find the probability that the committee will consist of four students.

An accountant found in a study that receivables fell into four categories: A: paid on time B: paid early C: paid late D: didn't pay Of a sample of 120 receivables she found that 35 were paid on time, 40 were paid early, 28 were paid late and the remainder were uncollectable. a) Using the results from the sample deter

Queueing Theory Question 1 An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane.

The probability of a bit error in a memoryless binary symmetric communication channel is 10^-3. Find the probability of a block of 1000 bits has five or more errors.

3. Let {N(t)}>0 be a renewal process for which the interarrival times {T1,T2,. . .} have cumulative distribution function F. Recall that the renewal function m(t) is given by m(t) E[N(t)j. (a) Find E[N(t)Ti=x] fort<x andfortx. (b) Find E[N(t)] E[E[N(t) T1]] to prove that m(t) satisfies the renewal equation m(t) F(t) + f m(t