Out of $40$ consecutive natural numbers,two are chosen at random. The probability that the sum of the numbers is odd is:

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

If three numbers are drawn at random successively without replacement from a set $S = \{1, 2, \ldots, 10\}$,then the probability that the minimum of the chosen numbers is $3$ or their maximum is $7$ is:

Cards are drawn one by one at random from a well-shuffled full pack of $52$ cards until two aces are obtained for the first time. If $N$ is the number of cards required to be drawn,then $P(N = n)$,where $2 \le n \le 50$,is

There are $10$ bulbs in a room,out of which $4$ are defective. If $3$ bulbs are chosen at random,what is the probability that the room will be illuminated? (The room is illuminated if at least one bulb is good.)

If two cards are drawn at random simultaneously from a well-shuffled pack of $52$ playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of $3$ is