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

By examining the chest X-ray, the probability that TB is detected when is actually suffering from TB is 0.99 the probability of a healthy person diagonosed to have TB is 0.001. In a certain city, 1 in 1000 persons suffer from TB. A person is selected at random and is diagonsed to have TB. What is the probability that he/she actually sufferes from TB?

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.

Suppose that 6% of the perons with blood group O are left handed and 10% of those with other blood groups are left handed. It is given that 30% of the persons have blood group O. if a left handed person is selected at random. What is the probability that the person has blood group O.

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 the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected. Of people free of HIV, 99% of the test are judged HIV–ive but 1% are diagnosed as showing HIV+ive. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the person actually has HIV?