There are 4 red marbles out of a total of 12 marbles. So, the probability of drawing red is $\frac{4}{12}$ = $\frac{1}{3}$.

The number of times in a period of 12 hours  the hands of the clock will form an acute angle will be the same as that for obtuse angle. So, you would think that the probability is  $\frac{1}{2}$. But if you take into account the number of times when the hands are alligned ( $0^{\circ }$), hands are at right angles and hands are facing in opposite directions ( ${180}^{\circ }$), then the probability would be slightly less than 0.5.

Sample space = total number of cards in deck = 52.

Favorable outcome (getting a spade) = 13.

Hence, P(getting a spade) = $\frac{13}{52}$ =  $\frac{1}{4}$.

Numbers divisible by 4 and 5 both = 20, 40, 60, 80, 100.

Hence P = $\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$ = $\frac{5}{100}$= $\frac{1}{20}$ 

= $\frac{1}{20}$

If a coin tossed thrice, the total possible outcomes = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}.

                                                                                 = 8

Number of cases of getting tail each time = {TTT}

                                                                  = 1

The probability of getting tail each time = $\frac{\text{Number of favourable cases}}{\text{total possible outcomes}}$

                                                               = $\frac{1}{8}$

Area of board = $\pi$ $R^2$  
Area of bull's eye = $\pi$ $r^2$  
Here, we shall use the concept of geometric probability as the number of outcomes are not finite.
$\text{The probability of hitting the bull's eye}$ 
$=\frac{\text{Area of the bull's eye}}{\text{Area of the board}}$=$\frac{\pi .r^2}{\pi .R^2}$ = $\frac{r^2}{R^2}$

The sum of the probabilities of all the elementary events of an experiment is 1.

Total number of pages in the book = 85
Favorable outcomes are: 8, 17, 26, 35, 44, 53, 62, 71, 80.
$\therefore$ No. of favorable outcomes = 9
Let $E$ be the event of getting sum of the digits on the page is 8.
$\text{Probability P(E)}$ = $\frac{\text{Number of outcomes favorable to E}}{\text{Number of all possible outcomes of the experiment}}=\frac{9}{85}$

$\text{Given: P(green marble)}=\frac{2}{3}$
Since there are 24 marbles, therefore the sample space will be 24 (i.e. the denominator must be 24.)
$\text{Let us assume there are}\text{x}\text{number of}\text{green marbles in the jar.}$
$\text{For an event E, probability}P\left(E\right)=\frac{\text{Number of outcomes favorable to E}}{\text{Number of all possible outcomes of the experiment}}$  
$\Rightarrow \text{P(green marbles)}=\frac{2}{3}=\frac{\text{x}}{24}$
$\Rightarrow \text{x}=16$
It implies that there are 16 green marbles in a jar of 24 marbles.
$\therefore \text{Number of blue marbles}=24-16=8.$