यदि 11 क्रमागत प्राकृतिक संख्याओं में से तीन संख्याएँ बिना पुनरावृत्ति के यादृच्छिक रूप से चुनी जाती हैं, तो उनके धनात्मक सार्व अंतर के साथ एक समांतर श्रेणी (A.P.) में होने की प्रायिकता क्या है?

A box contains 'x + 4' red, 'x – 1' green and 'x – 5' blue balls. If two balls are drawn from the bag one after another without replacement, then the probability of getting one red and one green ball is equal to the probability of getting a sum equal to or more than 8 when two fair dice are rolled. Find the probability of drawing a red ball when one ball is drawn at random from the bag.

Four persons are chosen at random from a group containing 3 men, 2 women, and 4 children. The probability that exactly two of them are children is: