List of top Quantitative Ability and Data Interpretation Questions on Probability asked in XAT

Steel Express stops at six stations between Howrah and Jamshedpur. Five passengers board at Howrah. Each passenger can get down at any station till Jamshedpur. The probability that all five persons will get down at different stations is:

Two teams, Arrogant and Overconfident, are participating in a cricket tournament. The odds that team Arrogant will be champion are 5 to 3, and the odds that team Overconfident will be champion are 1 to 4. What are the odds that either team Arrogant or team Overconfident will become the champion?

66. A management institute has six senior professors and four junior professors. Three professors are selected at random for a government project. The probability that at least one of the junior professors would get selected is:

A mother bought three shirts of the same colour but of different sizes, one each for her three sons. All three shirts were kept together in a box in a dark room. Each of the three boys took one shirt at random from the box. What is the probability that none of the boys ends up with his own shirt?