A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, is
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{1}{4}$
None of these
The probability of getting either all heads or all tails for exactly the second time in the $3^{rd}$ trial, if in each trial three coins are tossed, is
A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then the probability that $2$ are white and $1$ is red, is
Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is
A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is
In a lottery, a person choses six different natural numbers at random from $1$ to $20$ , and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [ Hint order of the numbers is not important.]