A box contains a normal coin and a two headed coin. A coin is selected at random and tossed. If heads appear, the other coin is tested, if tails appear, the same coin is tossed. (a) Find the probability that heads appear on the second toss. (b) If heads appeared on the second toss, find the probability that it also appeared on the first toss.

Q: In a random group of 5 individuals, what is the probability that at least two of them have the same…

A: We have given that the group of 5 individuals.

Q: Two regular 6-sided dice are tossed, one at a time. Compute the probability that the pips on both…

A: For each die, there are 6 possible outcomes.  So for 2 six-sided dice, there are 62=36 outcomes.…

Q: A department of commerce enrolls 125 students out of which 50 are girls. If 15 girls and 25 boys of…

A: It is given that, A department of commerce enrols 125 students out of which 50 are girls. It means…

Q: A golf ball is selected at random from a golf bag. If the golf bag contains 8 type A balls, 5 type B…

A: Number of type A balls = 8 Number of type B balls = 5 Number of type C balls = 3 Total number of…

Q: If one of these 210 individuals is selected at random, what is the probability that the person is a…

A: Here use Bayes Rule

Q: From a well-shuffled deck of ordinary playing cards, four cards are turnedover one at a time without…

A: A well shuffled deck of card contains 52 cards of which 26 cards are red and  13 card are spades.…

Q: Approximately 9% of people are left-handed. If two people are selected at random, what is the…

A:

Q: 66% of students at one college drink coffee, and 13% of people who drink coffee suffer from…

A: Given: Probability of students who drink coffee = 0.66 Probability of students who drink coffee…

Q: In a certain​ country, the true probability of a baby being a boy is 0.45. Among the next seven…

A:

Q: (a) Suppose that 10 % persons in a large group of people are obese. If persons are checked one by…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A fair 6-sided die is tossed and a four coloured spinner (blue, green, yellow, red) is spun. What is…

A: Given that A fair 6-sided die is tossed and a four coloured spinner (blue, green, yellow, red) is…

Q: The sex ratio of newborn human infants is about 105 males: 100 females. If four infants are chosen…

A: Given, sex ratio of newborn human infants is about 105 males: 100 females. sex ratio for male p =…

Q: In a nearby​ town, 68​% of adults have health insurance. If 7 adults are randomly selected from the​…

A: Here p =P(having health insurance) = 68% =0.68

Q: In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are…

A: Consider X be random variable which follows binomial distribution indicates the students belongs to…

Q: 4. The Traffic Violations Department receives 5 violations per hour, find the probability that it…

A:

Q: A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 8 type B…

A: Here  the golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, Then, total balls =…

Q: A tire company produced a batch of 5,500 tires that includes exactly 220 that are defective. If 4…

A: Obtain the probability that all the tires good. The probability that all the tires good is obtained…

Q: Two regular six sided dice are tossed, one at a time. compute the probability that the pips on both…

A: For each die, there are 6 possible outcomes.  So for 2 six-sided dice, there are 62=36 outcomes.…

Q: Two unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results…

A: It is given that Number of times two head occurs = 63 Number of times one head and one tail occurs =…

Q: A box contains 20 DVDS, 4 of which are defective. If two DVDS are selected at random (without…

A:

Q: At a car manufacturing plant, 10% of cars have some sort of defect when they come off the line. If…

A:

Q: A coin is flipped three times. If heads appears exaclty once, what is the probability that it…

A: The possible outcomes when a coin is flipped three times is,

Q: A lie detector is known to be 70% reliable when the person is quilty and 95% reliable when the…

A: The machine is reliable when person is guilty is 70% The machine is reliable when person is not…

Q: An unfair coin with​ Pr[H] = 0.75 is flipped. If the flip results in a​ head, a student is selected…

A: Given that the coin results in a Head.   we must choose from the class of fifteen boys and sixteen…

Q: In a second grade class containing 14 girls and 11 boys, 2 students are selected at random to give…

A:

Q: If there are, on the average, 7 defects in a new car, what is the probability that your new car has…

A: The Poisson distribution: A discrete random variable X is said to have a Poisson distribution with…

Q: In a certain country, the true probability of a baby being born a boy is 0.525% Among the next four…

A: Given that, Probability that a baby being born a boy is 0.525 Now, from the next four randomly…

Q: If a randomly selected person from the survey drives a what is the probability that he is a 'male"?

A: Solution

Q: In a large population, 66% of the people have been vaccinated. If 3 people are randomly selected,…

A: Let the random variable X denote the no. of people have been vaccinated and it follows binomial…

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: In the experiment of flipping a coin four times, what is the probability of obtaining odd number of…

A: Let A and B be two events with P(A) > 0. Then the conditional probability of B given A, denoted…

Q: (a) Suppose a mechanic begins to diagnose the problem by checking the spark plugs first and find…

A:

Q: A well-shuffled deck contains 52 cards. Suppose two decks are shuffled simultaneously and two cards…

A: Reviewing information, Cards in a deck =522 cards are drawn from 2 simultaneously shuffled decks

Q: What is the probability that a child expected from a certain family will be: a.) a boy b.) a girl.…

A: In this case, we need to find the probability that a child expected from a certain family will be a…

Q: At a car manufacturing plant, 20% of cars have some sort of defect when they come off the line. If…

A: Given dataProbability of defect in a car(p) = 0.20n = 99According to Binomial theoremProbability of…

Q: An urn contains 10 red balls, 20 yellow balls, and 40 orange balls.  If you reach into the urn and…

A:

Q: a certain population, a group of people has a 0.23% rate of heterochromia. If a random person is…

A: Probability = number of favorable eventstotal number of events

Q: What is the probability that, if three identical coins were flipped, all would end up heads? What is…

A: If three identical coins are tossed then the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH,…

Q: What is the probability that a five-card poker hand from a standard deck has two pairs of non-face…

A: There are 52 cards in a standard deck. 5 cards can be chosen in 525 ways Now, there are 4 face cards…

Q: When a single card is drawn from a well-shuffled deck of cards, what is the probability that it will…

A: Given, n = 52 cards single card is drawn.         To find, The probability that it will be an ace…

Q: A golf ball is selected at random from a golf bag. If the golf bag contains 8 type A​ balls, 5…

A: No.of type A balls =  8 No.of type B balls = 5 No.of type C balls = 6 Total number of balls =19…

Q: Suppose you roll a 6-sided die, a 10-sided die, and a 20-sided die. What is the probability that the…

A: Given that,  You roll a 6-sided die, a 10-sided die, and a 20-sided die.

Q: If a person in this town is selected at random, what is the probability that the individual is…

A: As per Bartleby guidelines, only one is to be answered; please upload the other separately. Given…

Q: If a ball is selected at random from an urn containing three red balls, two white balls, and five…

A: According to the provided information, there are 3 red balls, 2 white balls, and 5 blue balls

Q: A random sample of 15 persons is taken from a population in which 42% are Muslims. What is the…

A: It is given that a random sample of 15 persons is taken from a population in which 42% are Muslims.

Q: What is the probability that the first one selected is defective? What is the probability that the…

A: Let us define some events A : first one is defective B : second one is defective. Given that Number…

Q: A classroom has five students wearing glasses and 16 students not wearing glasses. If we randomly…

A:

Q: In a security check, it is known that out of 100 people, 2 persons bring things that are not allowed…

A: Probability distribution

Q: A box contains 20 DVDs, 4 of which are defective. If two DVDs are selected at random (without…

A: Given,no.of defective DVDs=4no.of good DVDs=16Total no.of DVDs=20

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.