Suppose we toss n balls into n bins one at a time uniformly at random. (a) What is the expected number of balls in the first bin? (b) What is the probability that every bin gets a ball?

Q: Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is…

A: Given:  100 people all toss a hat into a box and then proceed to randomly pick out a hat.  It is…

Q: Compute the expected number of people who are seated next to their spouse.

A: Solution: Given: A group of 2n people (n married couples) is randomly seated at a random table. We…

Q: Suppose that the New England Colonials baseball team is equally likely to win a game as not to win…

A: Given that the New England Colonials baseball team is equally likely to win a game as not to win it.…

Q: Suppose that the New England Colonials baseball team is equally likely to win a game as not to win…

A: Binomial distribution: The binomial distribution gives the probability of number of successes out of…

Q: A factory received a shipment of 15 capacitors, and the vendor who sold the items knows there are 8…

A: b) He can choose any 6 capacitors from 15 capacitors  in 15C6=5005 ways   He can choose 4 defective…

Q: What is the expected number of red balls when three balls are selected at random, with replacement,…

A: Given that the urn contains 4 red balls and 3 green balls So the total number of balls= (4+3)=7  If…

Q: A machine that manufactures automobile parts produces defective parts 15% of the time. If 8 parts…

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Q: A batch of 102 containers for frozen orange juice contains 19 that are defective. Two are selected,…

A: As per our guidelines, we are allowed to answer one question per query. Please post next question…

Q: 8. Vehicles entering an intersection from the east are equally likely to turn left, turn right, or…

A: If each trial has only two possible outcomes, that is, success and failure, the probabilities of…

Q: A coin is tossed four times. Assuming that the coin is equally likely to land on heads or tails,…

A: It is given that a coin is tossed 4 times. Since the coin is equally likely, the result can be heads…

Q: An assembly line machine produces a defective widget 23% of time,the rest of the time it produces a…

A: Here, n = 21 and p = 0.23.

Q: A baseball player has a .315 batting average. In other words, he gets a hit with probability 0.315…

A: (a) This is the case of binomial, as there are only two possible outcomes which are independent and…

Q: Suppose, a telephone exchange becomes very busy at a certain time of the day which is known as a…

A: Given,p=0.07q=1-pq=1-0.07=0.93A random variable X~Geometri distribution(p=0.07)P(X=x)=0.070.93x-1…

Q: In a lottery game, a player picks six numbers from 1 to 30. If the player matches all six numbers,…

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Q: A machine that manufactures automobile parts produces defective parts 11%of the time. If 8 parts…

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Q: A box contains eight different pairs of shocks. If four shocks are chosen at random without…

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Q: A production line produces resistors which are 4% defective. If a random sample of 150 resistors is…

A: It is given that 4% are defective that means p=0.04 The sample size is 150 so n=150 m=np=150×0.04=6…

Q: It is known that 25% of students in a particular village are smokers. A random sample of 20 of the…

A: From the given information, sample size n = 20 and p = 0.25.

Q: The probability that a certain machine turns out a defective item is 5%. Find the probability that…

A: The probability that the item is defective is 0.05. Sample size = n = 75.

Q: What is the theoretical probability of rolling a 8-sided die 2 times in a row, and all of them…

A: Sample space (S): Total possible outcome n(S) = 8*8 = 64

Q: A hospital switchboard receives an average of 4 emergency calls in 10 min. interval. What is the…

A: The average number of calls in 10 minutes is 4.

Q: A factory produces electronic components and defective components occur independently with…

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Q: It is known that 10% of all the items produced by a particular manufacturing process are defective.…

A: The probability that at least 35 of the selected items are defective =P[X>34] = 0.82034

Q: A card is randomly draw from a shuffled deck of cards and NOT REPLACED. A second card is drawn from…

A: Given Data; n(S)=52   Let A be the event of getting a red P(A)=26/52

Q: Suppose that 30% of all college freshmen gain weight. A sample of 20 selected randomly. What is the…

A: The random variable X is the college freshmen gain weight which follows binomial distribution with…

Q: An instrument for testing contaminated particles experiences errors 4 times on average during a…

A: Given Data: Let X represent the number of errors during 4-hour session X~ Poi(4)   Let Y represent…

Q: A die is rolled 30 times. What is the expected number of times that a 5 or 6 will appear?

A: There are 6 outcomes when a die is thrown.  the probability of getting 5 = 1/6  the probability of…

Q: When a new machine is functioning properly, only 3% of the items produced are defective. Assume that…

A: We are given,Probability of defective = p =3% = 0.03             Randomly selected sample size = n =…

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 19…

A: (a) Consider that shipment is accepted if no more than two defective pens

Q: Suppose a certain retail store has customers whose ages are normally distributed such that µ=37.5…

A: givenμ=37.5σ=7.6

Q: Suppose we toss n balls into n bins one at a time uniformly at random.  a.) What is the expected…

A: a. There are n balls to be placed into n bins. Each ball has equal probability to be in the bins.…

Q: A person invests $3 in a market in which he may gain $1 with probability or may lose $1 with…

A: Given data A person invests $3 in a market in which he may gain $1 with probability 1/2 or may lose…

Q: Let X be the number of heads obtained in 40 independent tosses of a fair coin. Then X is a binomial…

A: Given: Number of tosses (n) = 40 Coin is tossed independently.

Q: A machine that manufactures automobile parts produces defective parts 15% of the time. If 6 parts…

A:

Q: Suppose I randomly throw 10 balls into 4 bins (where each ball is thrown independently and uniformly…

A: Number of balls: m=10 Number of bins: n=4 (a) What is the expected number of empty bins: The…

Q: A box contains 15 red and 20 blue blocks. If 10 blocks are drawn at random from the pox, what is the…

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Q: A weighted die has probability 0.102 of landing on a 6. If you roll the die until you get a 6 for…

A: It is given that the probability of getting a 6 is 0.102.

Q: A bank has an average random arrival rate of 3.2 customers every 4 minutes. What is the probability…

A:

Q: When a bit is transmitted, it is received in error with probability p. Assume that 10 bits are…

A: Each of the bit is considered to be independently transferred and has a constant probability of p of…

Q: According to the statistics, 22% of cars in the city were at least 12 years old in 2004. Assume…

A:

Q: A researcher receives 100 containers of oxygen. Of those containers, 20 have oxygen that is not…

A: # Given: total no of oxygen container=100  no of ionised oxygen container=80  no of non ionized  =20…

Q: Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is…

A: Given that a box contains 6 cameras and that 3 of them are defective. So, (6-3)=3 are good and 3 are…

Q: A machine that manufactures automobile parts produces defective parts 13% of the time. If 8 parts…

A:

Q: Suppose 3% of items manufactured at a facility are defective. A random sample of 600 items are…

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Q: The probability of a radar station detecting an enemy plane is 0.65 and the probability of not…

A: We have to find expected no. Of stations detect plane.

Q: Suppose a fair dice is tossed into the air 10 times.For the overlapping number; a)what is the…

A: Givena) The probability of rolling a six when a fair dice is rolled p=16The probability of not…

Q: Find the probability that exactly four defectives are found

A: Given: A manufacturing process has 10% defective rate.  Random sample of 15 tubes

Q: Suppose a certain retail store has customers whose ages are normally distributed such that µ=37.5…

A: We have to find the probability that a randomly chosen customer is more than 48 years old..