A group of 12 students are located in the following time zones: 3 PST, 2 MST, 2 CST, 5 EST.Four students are randomly selected from this group. a) What is the probability that they are in the same time zone? b) What is the probability that they are all in different time zones? c) What is the probability that exactly two time zones will be represented in this group?

Q: In a study by the Department of Transportation, there were a total of 95 drivers that were pulled…

A: Given information- Total no. of drivers that were pulled over for speeding = 95

Q: 1. From a box containing five black balls and three green balls, three balls are drawn in…

A:

Q: If 8 different books are arranged at random on a shelf, what is the probability that a certain pair…

A: The number of books are 8.

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

A: Given Data: The probability that the student belongs to ethnic minorities is: p=33%=0.33 The total…

Q: What is the probability that the set selected contains the letter A and does not contain the letter…

A: Here An experiment consists of randomly selecting a set of 5 letters from the 26 letters in the…

Q: A school has 12 good runners of which 5 are girls. If four are chosen at random to represent the…

A: Given that a school has 12 good runners of which 5 are girls.  So (12-5)=7 are boys   We can select…

Q: Each main bearing cap in an engine contains four bolts. The bolts are selected at random, without…

A: A hypergeometric distribution plays an important role in theoretical distribution.This is a discrete…

Q: 2. One card is drawn from a standard pack of 52. What is the probability the it is either a Kina or…

A: no.of king cards=4no.of queen cards=4total no.of cards=52

Q: what is the probability that one or more of the selected companies are located in the said global…

A: Suppose 18 major computer companies operate in the Philippines and that 12 are located in Bonifacio…

Q: Find the probability of obtaining two heads in the toss of two unbiased coins when (a) at least one…

A:

Q: 1. Applicants for the presidency of the APIEMS job consists of 10 Filipinos, 8 Australians, 12…

A: Probability = Number of favourable outcome/Total number of outcomes

Q: Consider a collection of envelopes consisting of 1 red envelope,3 blue envelopes,3 green envelopes,…

A: Given that a collection of envelopes consisting of 1 red envelope,3 blue envelopes,3 green…

Q: Four cards are to be dealt successively at random and without replacement from an ordinary deck of…

A: Deck of card consists of 13 Spade cards. 13 diamond cards. 13 Club cards. 13 Heart cards.…

Q: A bowl contains 10 chips numbered 1, 2, . . . , 10, respectively. Five chips aredrawn at random, one…

A: Given: A bowl contains 10 chips numbered 1, 2, . . . , 10. So the number of chips, N=10. Five chips…

Q: its number is found divisible by 3. What is the probability that its number is also divisible by 5?

A: Here use basic probability  and Bayes rule

Q: An urn has 21 balls that are identical except that 8 are white, 8 are red, and 5 are blue. What is…

A: Given that ; An urn has 21 balls.  Total balls (n) = 21 White balls (w) = 8 Red balls (R) = 8 Blue…

Q: Suppose that a certain precinct contains 12 voters, of which 7 are Democrats and 5 are Republicans.…

A: From the given information, there are 7 Democrats and 5 are Republicans. The total number of voters…

Q: 2. A professor posts the grades for a class using the last four digits of the Social Security number…

A: Here Given Professor posts the grades for class using the last 4 digits of social security Number of…

Q: Suppose that 10 employees are to be divided among three jobs, with three employees going to job 1,…

A: Let us suppose there are three marbles viz. a red, a green and a blue. From these, there are three…

Q: Of the next 32 trials on the docket in a county court, 5 are homicides, 12 are drug offenses, 6 are…

A:

Q: An urn contains 7 white balls, 4 red balls, and 4 blue balls. What is the probability of selecting 9…

A: Given that  An urn contains White balls = 7 Red balls = 4 Blue balls = 4 Total balls in urn = 7 + 4…

Q: In a certain state, each automobile license plate number consists of two letters followed by a…

A:

Q: A presidential candidate plans to begin her campaign by visiting the capitals in 4 of 42 states.…

A: From thegiven  information  A presidential candidate plans to begin her campaign by visiting the…

Q: A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 42 states.…

A: Given data, Number of states (n) = 44 Number of states to be selected (r) = 3

Q: Suppose that 30% of people own dogs. If you pick two people at random, what is the probability that…

A: Let X be the number of dogs from binomial distribution with probability (p) = 30% = 0.30 and sample…

Q: From a box containing five black balls and three green balls, three balls are drawn in succession,…

A:

Q: Nine new employees, two of whom are married to each other, are to be assigned nine desks that are…

A: There are total 9 employees. We can arrange them in 1 row in 9!=362880 ways If the couple have…

Q: A bag contains 7 coins, of which 3 are fair; the remaining coin has a head on both sides. If a coin…

A: Concept of probability: Probability deals with the likelihood of occurrence of a given event. The…

Q: A jar holds 20 cookies, 15 are chocolate-chip cookies, and 5 are brussel-spout-with-turnip-chips…

A: We have to find given probability.

Q: 11. Of the 320 graduating students at a particular high school, 240 have applied to Universities,…

A: Given data: Total students=320 Students that have applied to Universities=240 Students that have…

Q: When 4 digits between 0 and 9 are randomly selected with replacement for a lottery ticket, what is…

A: From the provided information, Four digits between 0 and 9 are randomly selected with replacement…

Q: 4. What is the probability that in a family of 3 children, at least two are girls? 5. What is the…

A: The specified probability for a number of events, where a specific number of boys or girls occur in…

Q: A jury of 6 members is to be selected from a panel consisting of 8 men and 8 women. a. How many…

A: Given :Number of man = 8 Number of females = 8 Total number of members = 8+8=16 We want to choose…

Q: From a sack of fruit containing 10 oranges, 4 apples, and 6 bananas, a random sample of 8 pieces of…

A:

Q: A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic…

A: From the provided information, A company that produces fine crystal knows from experience that 10%…

Q: 8. In a class of 16 students, 4 are undergrads. For the final project, students are randomly divided…

A: Probability:           Probability is deals with the random occurrence of events is known as…

Q: One-fourth of the female freshmen entering a Virginia College are out-of-state students. If the…

A: Binomial distribution is given by

Q: If an urn has five white balls and 10 red balls what is the probability that five randomly selected…

A: Given that an urn has 5 white balls and 10 red balls. Total number of balls is 5+10=15 Number of…

Q: 4) A committee of 7 is to be randomly selected from a small company employing 10 Engineers, 4…

A: It is given that Number of engineers = 10 Number of non-engineers = 4+6+5 = 15 Total = 10+15 = 25…

Q: 8. Seven new employees, two of whom are married to each other, are to be assigned seven desks that…

A:

Q: If an urn has 10 white balls and nine red balls what is the probability that five randomly selected…

A: Total number of white balls = 10 The probability of white ball = 10/19 = 0.526   n = 5

Q: A standard provincial landline telephone number in Cavite contains area code of 3 digits and…

A:

Q: In a study by the Department of Transportation, there were a total of 89 drivers that were pulled…

A: a) There are total 89 drivers, among which 36 men were ticketed and 15 men were not ticketed.

Q: An engineering company has four openings and the applicant pool consists of 6 database…

A: Hey, since there are multiple subparts posted, we will answer the first three subparts. If you want…

Q: A committee of size 5 is to be selected from a group of 6 men and 9 women. If the selection is made…

A: There are totally 15 people in which 6 are men and 9 are women. The number of ways selecting…

Q: From a group of 50 students at a university (10 students per year) a coordinating committee of 4…

A: Answer : - Given,   a group of 50 students at a university (10 students per year).…

Q: Of the 28 restaurants in an area, 4 serve one type of cuisine, 9 serve two different types of…

A: We have to find given probability.

Q: and 7 fed Dals, the second urn has 2 blue balls and 8 red balls, and the third urn has 5 blue balls…

A: Answer: If we draw a red from the first urn then it is sure that we will draw at least 2 balls…

Q: Suppose that 40% of Tulane undergraduates intend to continue on to graduate school after completing…

A: From the provided information, 40% of Tulane undergraduates intend to continue on to graduate school…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.