In a class,there are $15$ boys and $10$ girls. Three students are selected at random. The probability that $1$ girl and $2$ boys are selected,is

Consider the circuit shown in the image. If the probability that each switch is closed is $p$,then find the probability of current flowing through $AB$.

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

In a class of $25$ students with roll numbers $1$ to $25,$ a student is picked up at random to answer a question. Find the probability that the roll number of the selected student is either a multiple of $5$ or $7$.

$A$ 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:

$3$ coins are tossed. Find the probability of getting at least $2$ heads.