Probabilities

Question 1

In how many ways can a panel of 5 judges make a majority decision?

Answer 1

16

Question 2

A box contains 7 – 25 KW lamps, 5 – 40 KW lamps and 4 – 60 KW lamps. All the lamps are of the same shape and size. If a lamp is taken at random from the box, what is the probability that the lamp is a 25 KW or a 60KW?

Answer 2

11/16

Question 3

A box contains 7 – 25 KW lamps, 5 – 40 KW lamps and 4 – 60 KW lamps. All the lamps are of the same shape and size. If 2 lamps are taken from the box at random without replacement, what is the probability that both lamps are 40KW?

Answer 3

1/12

Question 4

A box contains 7 – 25 KW lamps, 5 – 40 KW lamps and 4 – 60 KW lamps. All the lamps are of the same shape and size. If 2 lamps are taken from the box at random with replacement, what is the probability that both lamps are of the same wattage?

Answer 4

45/128

Question 5

A certain kind of tire has a life exceeding 30,000 miles with probability 0.80. What is the probability that a set of these tires on a car, all will last longer than 30,000 miles?

Answer 5

0.4096

Question 6

A number consisting of three different digits is to be formed using the integers 2, 3, 4, 6, 7, 8. How many of the numbers are greater than 700?

Answer 6

40

Question 7

A number consisting of three different digits is to be formed using the integers 2, 3, 4, 6, 7, 8. How many numbers are odd?

Answer 7

40

Question 8

A number consisting of three different digits is to be formed using the integers 2, 3, 4, 6, 7, 8. How many numbers begin and end with an even number?

Answer 8

48

Question 9

A basketball team consists of two centers, four forwards and four guards. In how many ways can a coach select a starting five of one center, two forwards and two guards?

Answer 9

72

Question 10

A company produces fuses that are packages in boxes of 120. If the production line is known to produce 2% defective fuses on the average, what is the probability that a randomly selected box will contain 5 defective fuses?

Answer 10

0.0597

Question 11

A company produces fuses that are packages in boxes of 120. If the production line is known to produce 2% defective fuses on the average, what is the probability that a randomly selected box will contain no defective fuses?

Answer 11

0.0885

Question 12

Mc Naldos’ Deli offers a lunch special in which you can choose a sandwich, a side dish, and a beverage. If there are 10 different sandwiches, 12 different side dishes, and 7 different beverages from which to choose, how many lunch specials can you order?

Answer 12

840

Question 13

The odds that Mario wins a certain game with a prize of P10,000 are 5 to 7. What is his mathematical expectation?

Answer 13

P 4, 167

Question 14

Compute the total number of 8–letter arrangements of the letters of the word PARALLEL.

Answer 14

3, 360

Question 15

How many different ways can 3 red, 4 yellow, and 2 blue bulbs be arranged in a string of Christmas tree lights with 9 sockets?

Answer 15

1, 260

Question 16

The CIT–U CE department has 15 faculty members. Four are to be selected to attend the CE convention. How many ways can the school select the 4 members if 2 of them are best friends and may or may not attend together?

Answer 16

793

Question 17

From 7 men and 5 women, a committee of four is chosen by lot. What is the probability that the committee will involve all men or all women?

Answer 17

8/99

Question 18

The probability that the wife will be alive in 20 years is 0.8 and the probability that the husband will be alive in 20years is 0.70.What is the probability that at least one of them will be alive in 20 years?

Answer 18

0.94

Question 19

Four cards are drawn together from a deck of 52 cards. Find the probability that all are of the same suit.

Answer 19

0.01056

Question 20

In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a round table if those of the same nationality sit together?

Answer 20

41, 472

Question 21

In the CE Board Exam in which there are 3 subjects, the probability of a student passing any subject is 0.70. What is the probability that the student passes at least 2 subjects?

Answer 21

0.784

Question 22

There are 3 candidates A, B, and C for a Mayor in a small Town. The odds that A will win are 4:3 and the odds that B will win are 1:5. What is the probability that B or C will win?

Answer 22

3/7

Question 23

In a survey involving the votes received by 3 barangay councillors A, B, and C last 2016 Barangay elections revealed the following results:
50 voted the 3 candidates
600 voted A
770 voted B
700 voted C
300 voted A and B
420 voted B and C
240 voted A and C
How many in the group voted candidate A only?

Answer 23

110

Question 24

A roulette circle is divided into 10 sectors with 1 of the sectors coloured white, 2 of the sectors coloured red, 3 coloured blue, and 4 coloured black. A spinner wins P 500 if she spins white, P 400 if she spins red, P 300 if spins blue, and P 200 if spins black. What is the mathematical expectation of the game?

Answer 24

300

Question 25

A signal is to be formed from 4 different colored flags hung on a horizontal line. How many signals can be formed, if the signal is to consist of one or more flags?

Answer 25

64