Four boys and three girls stand in a queue for an interview. What is the probability that they will stand in alternate positions?

$A$ six-faced die is biased such that it is twice as likely to show an even number as an odd number when thrown. If it is thrown twice, what is the probability that the sum of the two numbers obtained is even?

One bag contains $5$ white and $3$ black balls and a second bag contains $2$ white and $4$ black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?

Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$?

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is ${P_1}$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is ${P_2}$. Then: