$A$ family with three children is chosen at random. The probability that the oldest and youngest children are of the same gender is

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2, \sqrt{3N}, N + 2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is

$A$ bag contains $3$ white,$2$ blue,and $5$ red balls. One ball is drawn at random from this bag. The probability that the ball drawn is not red is

One card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is a face card (Jack,Queen,and King only) is

$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

The probability of obtaining an even prime number on each die,when a pair of dice is rolled is