In a group of 30 scientists working on an experiment, 20 never commit error in their work and are reporting results elaborately. Two scientists are selected at random from the group. Find the probability distribution of the number of selected scientists who never commit error in work and reporting.

There is a group of 50 people who are patriotic out of which 20 believe in non-violence. Two persons are selected at random out of them, write the probability distribution for the selected persons who are non-violent. Also find the mean of the distribution. Explain the importance of non-violence in patriotism.

Two numbers are selected at random from first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of X. find the mean and variance of this distribution.

Of the students in a college, it is known that 60% reside in hostel and 40% are day-scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day-scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade. What is the probability that the student is a hostlier ?

Textbooks on science may give you a wrong impression that studying science is dry and all too serious and that scientists are absent-minded introverts who never laugh or grin. This image of science and scientists is patently false. Scientists, like anyother group of humans, have their share of humorists, and many have led their lives with a great sense of fun and adventure, even as they seriously pursued their scientific work. Two great physicists of this genre are Gamow and Feynman. You will enjoy reading their books listed in the Bibliography.

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

A scientist is weighting each of 30 fishes. Their mean weight worked out as 30 gm and standard derivation of 2gm. Later, it ways found that the measuring scale was misaligned and always under reported every fish by 2gm. The correct mean and standard deviation (in gm) of fishes are respectively :