Level of Difficulty

Three groups of children contain respectively $3$ girls and $1$ boy, $2$ girls and $2$ boys, and $1$ girl and $3$ boys. One child is selected at random from each group. The probability that the three selected consists of $1$ girl and $2$ boys is:

A bag contains $5$ black and $3$ red balls. A ball is taken out of the bag and is not returned to it. If this process is repeated three times, then what is the probability of drawing a black ball in the next draw of a ball?

A bag contains $5$ black and $3$ red balls. A ball is taken out of the bag and is not returned to it. If this process is repeated three times, then what is the probability of drawing a red ball?

In a room, there are $7$ persons. The chance that two of them were born on the same day of the week is

In a hand at a game of bridge, what is the chance that the $4$ kings are held by a specified player?

One hundred identical coins each with probability $P$ of showing up Heads are tossed once. If $0<P<1$ and the probability of Heads showing on $50$ coins is equal to that of Heads showing on $51$ coins, the value of P is

Two small squares on a chess board are chosen at random. Find the probability that they have a common side:

The probabilities of A, B, and C solving a problem $\frac{1}{3}, \frac{2}{7}$ and $\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.