The Mathematics of Maybe: Introduction to Probability

A coin is tossed $1000$ times with the following frequencies: Head: $455$, Tail: $545$. What is the probability of getting a tail?

Which of the following describes an event with a probability of $0.5$?

If $P(E) = 0.72$, what is the value of $P(\text{not } E)$?

In a spinning wheel with $8$ equal sectors numbered $1$ to $8$, what is the probability of the pointer landing on a number divisible by $4$?

A box contains cards numbered from $1$ to $50$. A card is drawn at random. What is the probability that the number on the card is a prime number such that the sum of its digits is an even number?

In a deck of $52$ cards, what is the probability of drawing a red face card (King, Queen, or Jack)?

There are $30$ students in a class. If $12$ of them are girls, what is the probability that a student chosen at random is a boy?

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

The sum of probabilities of all elementary events of an experiment is:

A bag contains 3 red, 5 black, and 7 white balls. A ball is drawn at random. What is the probability that it is white?

What is the probability of getting a sum of $2$ when two coins are tossed?

In a bag of $20$ balls, $4$ are blue. If one ball is drawn, what is the probability that it is NOT blue?

A die is thrown once. What is the probability of getting an even prime number?

A card is drawn from a deck of $52$ cards. What is the probability of getting a spade?

If the probability of an event $E$ is $P(E)$, then which of the following is true?

A bag contains $10$ red, $20$ blue and $30$ green balls. A ball is drawn at random. What is the probability that it is a blue ball?

In $100$ tosses of a coin, tails occurred $52$ times. Find the probability of getting a head.

A set of data contains 2000 observations. The experimental probability of an observation being less than 50 is 0.4, and the probability of it being greater than 70 is 0.35. How many observations lie in the range [50, 70]?

If the probability of success of an experiment is $0.7$, and it is conducted 500 times, find the difference between the expected frequency of success and failure.

Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is a perfect square?

A box contains cards numbered $1$ to $50$. If one card is drawn, what is the probability that it has the number $25$?

If a coin is tossed, what is the probability that it shows a head and a tail at the same time?

Which of the following is an impossible event when rolling a single standard die?

In a bag, there are $2$ red, $3$ blue, and $5$ green marbles. What is the probability of picking a blue marble?

If the probability of occurrence of an event is $p$, then the probability of its non-occurrence is:

Which of the following is the sample space for tossing a coin and rolling a die simultaneously?

In $1000$ trials of an experiment, an event $E$ occurs $350$ times. The empirical probability of $E$ is:

A box contains 100 tickets numbered 1 to 100. A ticket is drawn at random. What is the probability that the number on the ticket is a prime number less than 30?

Two dice are rolled. What is the probability that the sum is a multiple of 5?

What is the probability that a leap year has 53 Sundays?

A tree diagram starts from a single point. What is this point usually called in diagram theory?

If you have a choice of 3 fruits (Apple, Banana, Orange) and 2 drinks (Milk, Juice), how many possible snack combinations exist?

In a family of two children, what is the probability of having two boys $(BB)$ according to a tree diagram?

If you roll a die and then roll it again, how many total outcomes are in the complete tree diagram?

Two coins are tossed. Using a tree diagram, what is the probability of getting a result where both tosses are the same (both heads or both tails)?

A tree diagram shows two stages of a game. Stage 1 has 2 outcomes and Stage 2 has 5 outcomes. How many total possible final outcomes are there?

If you toss a coin twice, the probability of getting at least one tail is calculated by subtracting which outcome's probability from 1?

A jar contains $2$ orange, $3$ purple, and $5$ white marbles. If two marbles are drawn with replacement, what is the probability that at least one is white?

There are $3$ paths from A to B and $2$ paths from B to C. One path from A to B is closed for repairs. What is the probability that a person choosing paths at random can still get from A to C?

A player tosses a fair coin. If it's heads, they score $2$ points. If it's tails, they score $1$ point. What is the probability that after $2$ tosses, their total score is exactly $3$?