Probability and Statistics
If a school buys three computers a, b, and c pesos each, gets a discount of 90%, which expression would determine the average price paid by the school?
A. (a+b+c) 0.9/3
Hotels, like airlines, often overbook, relying on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservation will not be used. If 4 reservations are made, what is the probability fewer than two will cancel?
A. 0.8192
At a conference, after everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged. How many were at the conference?
A. 10
In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?
A. 1152
In how many ways can 5 people line up to pay their electric bills?
A. 120
In mathematics examination, a student may select 7 problems from a set of 10 problems. In how many ways can he make his choice?
A. 120
The value of 5! is equal to:
A. 120
Six non-parallel lines are drawn in a plane. What is the maximum number of point of intersections of these lines?
A. 15
The probability for EE board examinees from a certain school to pass Mathematics is 3/7 and that for ESAS is 5/7. If none of the examinees failed in both subjects and there are 4 examinees who pass both subjects, how many examinees from the school took the examination?
A. 28
A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One marble is selected at random. What is the probability the the marble is blue?
A. 3/8
A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle?
A. 55/64
How many permutations can be done from the letters of the word BANANA?
A. 60
A card is chosen from pack of playing cards. What is the probability that it is either red or a picture card?
A. 8/13
The mean duration of television commercials on a given network is 75 seconds, with a standard deviation of 20 seconds. Assume that duration time is approximately normally distributed. What is the approximate probability that a commercial will last less than 35 seconds?
B. 0.025
From past experience it is known 90 percent of one year old children can distinguish their mother's voice of a similar sounding female. A random sample of 20 one-year's old are given this voice recognize test. Find the probability that at least 3 children did not recognize their mother's voice.
B. 0.323
You are given n=5 measurements 2,1,1,3,5. Find the sample standard deviation.
B. 1.673
From past experiments, it is known 90% of one year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their Mother's voice. Find the mean of x.
B. 2
A guy has 8 flowers of different variety. In how many ways can he select 2 or more flowers to form a bouquet?
B. 247
A student did not study for his upcoming examination on which is 15 multiple choice test questions, with five possible choices of which only one is correct, what is the expected number of correct answers he can get?
B. 3
Five different books (A,B,C,D and E) are to be arranged on a shelf. Books C and D are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and E may be arranged is
B. 3!
A single card is drawn from an ordinary deck of card 52 cards. Find the probability p that the card is face card and a heart.
B. 3/52
How many ways can you arrange the word "MONDAY" wherein the letters are taken at a time?
B. 360
Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags?
B. 64
In how many ways can 5 people line up to pay their electric bills, if two particular persons refuse to follow each other?
B. 72
A secondary school is contracting its alumni asking for donations to help put up new computer laboratory. Past records show that 80% of the alumni will make a contribution of at least P50.00. A random sample of 20 alumni is selected. What is the probability that exactly 15 alumni will make a donation of at least P50.00?
C. 0.174
The mean computer usage of a person is 8 hours with a standard deviation equal to 1.5 hours. Assume that the computer usage is approximately normally distributed. What is the probability that a person will use the computer for at least 8.5 hours?
C. 0.37
If a quiz consists of four true-false questions, and a student guesses at each answer, what is the probability the student answers exactly half of the questions correctly?
C. 0.5000
An urn contains 4 black balls and 6 white balls. What is the probability of getting one black and one white ball in two consecutive draws from the urn?
C. 0.53
A fair coin is tossed three times. Find the probability that there will appear three heads.
C. 1/8
The median of the following numbers: 8 8 9 10 12 13 14
C. 10
In how many ways can 4 coins be tossed?
C. 16
You are given n=5 measurements 2,1,1,3,5. Find the sample variance.
C. 2.8
A class of 40 took examination in Algebra and Trigonometry. If 30 passed Algebra, 36 passed Trigonometry, and 2 failed in both subjects, the number of students who passed the two subject is:
C. 28
How many ways can you invite one or more of five friends to the party?
C. 31
A semiconductor company will hire 7 man and 4 women. In how many ways can the company choose from 9 man and 6 women who qualified for the position?
C. 540
How many permutations are there if the letters PNRCSE are taken six at a time?
C. 720
How many ways can 7 people be seated at a round table?
C. 720
Each of the question on a quiz is a five-part multiple choice question with exactly one correct answer. A student, totally unprepared for the quiz, guesses on each of 15 questions. If at least 11 questions must be answered correctly to pass the quiz, what is the chance the student passes?
D. 0
From past experience, it is known 90% of one year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother's voice.
D. 0.122
Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to he drug test (N). Assume the possible combinations of the three students' drug test evaluation as PPP, PPN, PNP, NPP PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that all three students get positive results?
D. 1/8
Find the mean, median and mode respectively of the following numbers: 13, 13, 14, 12, 11, 10, 9, 11, 8, 11, 5, and 15.
D. 11, 11, 11
In a class of 40 students, 27 lie Calculus and 25 like Geometry. How many students liked both Calculus and Geometry?
D. 12
A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both?
D. 13
What is the average value of 7/8 ad 3/4?
D. 13/16
In how many ways can 9 books be arranged on a shelf so that 5 of the books are always together?
D. 14,400
How many distinct permutations can be made from the letters of the word INFINITY?
D. 3360
In order to pass a certain exam, candidate must answer correctly 70% of the test questions. If there are 70 questions on the exam, how many questions must be answered correctly in order to pass?
D. 49
In how many ways can 6 distinct books be arranged in a bookshelf?
D. 720
The plate number of a vehicle consists of a 5-alphanumeric sequence is arranged such that the first two characters are alphabet and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and repetitions are not allowed?
D. 90000
During an examination, the following scores are collected: 0 8 9 11 12 13 18 18 20. If there was an error in encoding where one "18" should be "16", which of the following is affected?
D. mean and standard deviation
