If there of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is

Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8 . Then, the probability that the problem is solved correctly by atleast one of them, is

A fair die is rolled. The probability that the first time 1 occurs at the even throw, is

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is

If 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains excatly 3 balls, is

Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r1 , r2 and r3 are the numbers obtained on the die, then the probability that ω^r1+ω^r2+ω^r3=0 , is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is