Probability - A Theoretical Approach

Which of the following assumption needs to be done in dealing with the theoretical probability.

You buy a lottery ticket and win the jackpot.

If $A$ and $B$ are mutually exclusive events $P\left(A\right)=\frac{3}{8}$ and $P\left(B\right)=\frac{1}{8}$, then find $P\left(\overline{A}\right)$.

On one page of a telephonic directory, there were $200$ telephone numbers. The frequency distribution of their unit place (for example, in the number $25828573$, the unit place digit is $3$) is given below.

Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is $5$?

All jacks, queens and kings are removed from a pack of $52$ cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is a red card.

A student made a cube shaped die from a card sheet. Instead of writing numbers $1, 2, 3, 4, 5, 6$ on its faces, he wrote letters $a, b, c, d, e, f$ one on each face, randomly. If he rolls the die twice, find the probability that he gets a vowel on the upper face both times.

A cubical die numbered from $1$ to $6$ are rolled twice. Find the probability of getting the sum of numbers on its faces is $10$.

Which of the following cannot be the probability of an event?

Define three rules of probability.

Define probability.

The probability of guessing the correct answer to a certain question is $\frac{x}{2}$. If probability of not guessing the correct answer is $\frac{2}{3}$, then find $x$.

A bag contains $12$ balls out of which $y$ are black if $6$ more black balls are put in the bag, the probability of drawing a black ball will be double than that of find the value of $y$.

A bag contains $12$ balls out of which $y$ are black If a ball is drawn at random, what is the probability that it will be a black ball?

A bag contains $5$ red balls and some white balls. If the probability of drawing a white ball is double that of a red ball, find the number of white balls in the bag.

A bag contains $4$ red, $5$ black and $3$ yellow balls. A ball is taken out of the bag at random. Find the probability that the ball taken out is of not of red colour.

A bag contains $4$ red, $5$ black and $3$ yellow balls. A ball is taken out of the bag at random. Find the probability that the ball taken out is of yellow colour.

Cards marked with numbers $1, 2, 3, 4, ......, 20$ are well shuffled and a card is drawn at random. What is the probability that the number on the card is a perfect square?

Cards marked with numbers $1, 2, 3, 4, ......, 20$ are well shuffled and a card is drawn at random. What is the probability that the number on the card is divisible by $3$.

Cards marked with numbers $1, 2, 3, 4, ......, 20$ are well shuffled and a card is drawn at random. What is the probability that the number on the card is a prime number.

From a pack of $52$ playing cards all cards whose numbers are multiples of $3$ are removed. A card is now drawn at random. What is the probability that the card drawn is an even numbered red card?