A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then
${P_1} = {P_2}$
${P_1} > {P_2}$
${P_1} < {P_2}$
None of these
Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is
Three integers are chosen at random from the first $20$ integers. The probability that their product is even, is
Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?
$n$ cadets have to stand in a row. If all possible permutations are equally likely, then the probability that two particular cadets stand side by side, is
Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket . If the probability that all the tickets go to the children of the family $B$ is $\frac {1}{12}$ , then the number of children in each family is?