A university has to select an examiner from a list of 50 persons, 20 of them are women and 30 men, 10 of them knowing Hindi and 40 not, 15 of them being teacher and the remaining 35 not. What is the probability of the two university selecting a Hindi knowing women teacher?

A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man?

A committee of two is selected from two men and two women. What is the probability that the committee will have : two men ?

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?

40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostlers got A grade while from outside students, 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hostler ?

In a group of 400 people, 160 are smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is smoker and non vegetarian ?

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years ?

A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B is chosen. If two balls are drawn at random from the selected bag, find the probability of one of them being red and the other black.

There are 40 scholars in a class, out of which 10 are sports- persons. Three scholars are selected at random out of them. Find the probability distribution for the selected persons who are sports-persons. Find the mean of the distribution.