$A$ fair coin is tossed repeatedly. If a tail appears on the first four tosses,then the probability of a head appearing on the fifth toss equals:

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S = \{x \in \mathbb{Z} : x(66 - x) \geq \frac{5}{9} M\}$ and the event $A = \{x \in S : x \text{ is a multiple of } 3\}$. Then $P(A)$ is equal to

If three students $A, B, C$ independently solve a problem with probabilities $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively,then the probability that the problem will be solved is

Let $S_n = \sum_{k=1}^n k$ denote the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it is

From the word $POSSESSIVE$,a letter is chosen at random. The probability of it being $S$ is

$A$ fair coin and an unbiased die are tossed. Let $A$ be the event 'head appears on the coin' and $B$ be the event '$3$ on the die'. Check whether $A$ and $B$ are independent events or not.