Statistics

A survey of \(100\) persons revealed that \(72\) of them had eaten at restaurant P and that \(52\) of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q?

The probability for the ECE board examinees from a certain school to pass the subject Mathematics is \(3/7\) and for the subject Communications is \(5/7\). If none of the examinees fails both subject and there are \(4\) examinees who pass both subjects, find the number of examinees from that school who took the examinations.

How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word "personnel"?

Five different mathematics books, \(4\) different electronics books and \(2\) different communications books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed.

The number of ways can \(3\) nurses and \(4\) engineers be seated on a bench with the nurses seated together is

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?

In how many ways can \(4\) boys and \(4\) girls be seated alternately in a row of \(8\) seats?

How many different ways can \(5\) boys and \(5\) girls form a circle with boys and girls alternate?

In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers?

A semiconductor company will hire \(7\) men and \(4\) women. In how many ways can the company choose from \(9\) men and \(6\) women who qualified for the position?

There are \(13\) teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they all play without any team playing more than one game in any day?

There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice?

There are \(50\) tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns \(5\) tickets?

Determine the probability of drawing either a king or a diamond in a single draw from a pack of \(52\) playing cards.

A card is drawn from a deck of \(52\) playing cards. Find the probability of drawing a king or a red card.

The probability of getting at least \(2\) heads when a coin is tossed four times is,

The probability of getting a credit in an examination is \(1/3\). If three students are selected at random, what is the probability that at least one of them got a credit?

In the ECE Board Examinations, the probability that an examinee will pass each subject is \(0.8\). What is the probability that an examinee will pass at least two subjects out of the three board subjects?

In a multiple choice test, each question is to be answered by selecting \(1\) out of \(5\) choices, of which only \(1\) is right. If there are \(10\) questions in a test, what is the probability of getting \(6\) right of pure guesswork?

A bag contains \(3\) white and \(5\) black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?