Probability

A die is thrown. What is the sample space $S$ for the event 'getting a number less than 1'?

In a family with 3 children, what is the sample space for the number of girls?

A spinner has 4 colors: Red, Blue, Green, Yellow. If it is spun once, what is the size of the sample space?

What is the sample space for selecting a perfect square from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$?

A box contains 3 slips numbered 1, 2, 3. Two slips are drawn one after another without replacement. The sample space is:

An experiment consists of rolling a die and then drawing a card from a set of 3 cards labeled $X, Y, Z$. What is the total number of outcomes in the sample space?

A pair of dice is rolled. How many elements are in the sample space where the sum of the two numbers is at most 4?

An experiment consists of flipping a coin. If it is Heads, you flip it again. If the second flip is also Heads, you flip it a third time. If any flip is Tails, you roll a die and stop. What is the total number of outcomes in the sample space?

How many paths are there from $(0,0)$ to $(3,3)$ if you can only move one unit Right or one unit Up at each step?

A man has 4 keys in his pocket, only one of which opens his door. He tries the keys one by one without replacement until the door opens. The sample space is the set of all possible sequences of keys tried. How many outcomes are in $S$?

If $P(A) = \frac{1}{4}$, what is $P(A')$?

If two coins are tossed, what is the probability of getting at most one tail?

A die is thrown once. What is the probability of getting a number greater than or equal to 2?

What is the probability of picking the King of Diamonds from a standard deck of cards?

Two dice are thrown. What is the probability that the difference of the numbers on the two dice is 2?

If $A$ and $B$ are any two events such that $P(A) = 0.6$ and $P(B) = 0.7$, what is the minimum possible value of $P(A \cap B)$?

A number is selected at random from the first 30 natural numbers. What is the probability that it is a composite number?

There are 5 red and 5 blue shoes in a closet. If 4 shoes are picked at random, what is the probability that there is at least one pair (one red and one blue of the same size)? (Assume there are 5 distinct sizes)

If $x_1, x_2, x_3$ are non-negative integers such that $x_1 + x_2 + x_3 = 10$, what is the probability that $x_1$ is an even number?

Three distinct numbers are selected from the set $\{1, 2, \dots, 9\}$. What is the probability that their product is even?

If $P(A \cup B) = 0.8$, $P(A) = 0.5$, $P(B) = 0.6$, then $P(A \cap B)$ is:

The probability of getting a tail in a single toss of a coin is:

If $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cup B) = 0.9$, then the event $A \cap B$ is:

In a deck of 52 cards, the probability of drawing either a King or a Queen is:

Three events $A, B, C$ are mutually exclusive. $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{3}$. Find $P(C)$ if the three events are also exhaustive.

For two events $A$ and $B$, $P(A' \cup B') = 0.7$ and $P(A) = 0.5$. Find $P(A \cap B')$.

A bag contains 5 red and 3 blue balls. If two balls are drawn at random, what is the probability that both are red?

If $P(A \cup B) = 0.6$ and $P(A \cap B) = 0.2$, find $P(A') + P(B')$.

If $P(A) = p$ and $P(B) = q$, then the probability $P(A \cup B)$ is at most:

Given $P(A) = 0.5, P(B) = 0.3, P(C) = 0.2$ for three mutually exclusive events, find $P(A' \cap B' \cap C')$.

A coin is tossed three times. What is the probability of getting no tails?

A number is chosen from $\{1, 2, ..., 30\}$. What is the probability that it is a perfect square?

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a club or an ace?

A letter of the English alphabet is chosen at random. What is the probability that it is a letter found in the word 'APPLE'?

A pair of dice is rolled. What is the probability that the sum is neither 7 nor 11?

What is the probability that a randomly chosen two-digit number is a multiple of 10?

If $A$ and $B$ are two events such that $P(A) = 0.4$, $P(B) = 0.8$ and $P(B/A) = 0.6$ (Conditional notation context in Grade 11: $P(A \cap B) = 0.24$), find $P(A \cup B)$.

If the odds in favor of an event $A$ are $2:3$ and the odds against event $B$ are $3:7$, what is the maximum possible value for $P(A \cup B)$?

From the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, two digits are selected at random. What is the probability that their sum is even given that the digits are distinct?

There are 4 envelopes and 4 letters addressed to different people. If the letters are placed in the envelopes at random, what is the probability that no letter is placed in the correct envelope?

In a single throw of two dice, what is the probability of getting a sum of $2$?

A letter is chosen at random from the word 'MATHS'. What is the probability that it is 'M'?

If $E$ is an event, then $P(E) + P(E')$ is equal to:

The set $\{H, T\}$ is the sample space for which experiment?

A bag contains $5$ white and $3$ black balls. Two balls are drawn at random without replacement. What is the probability that both are black?

If $P(A) = 0.6, P(B) = 0.5$ and $P(A \cap B) = 0.2$, find $P(A \cup B')$.

If $A$ and $B$ are any two events, then $P(A \cap B) + P(A \cap B')$ is equal to:

Two numbers $x$ and $y$ are selected at random from the set $\{1, 2, 3, \dots, 3n\}$. Find the probability that $x^2 - y^2$ is divisible by 3.

In a group of 100 students, 60 like math, 40 like science, and 20 like both. If a student is chosen at random, find the probability that the student likes neither math nor science.

A and B are two events such that $P(A) = 0.54$, $P(B) = 0.69$ and $P(A \cap B) = 0.35$. Find $P(A \cup B')$.

The probability of the sample space $P(S)$ is always:

If $A$ and $B$ are mutually exclusive, can they occur at the same time?

If an event is certain to occur, its probability is:

If $S = \{HH, HT, TH, TT\}$, the event $E = \{HH\}$ is a:

Two coins are tossed. Let $A = \{HH, HT\}$ and $B = \{HH, TH\}$. Find the event representing $A - B$.

If a sample space $S = \{1, 2, 3, 4\}$, which of the following set of events is exhaustive?

Two events $A$ and $B$ are such that $P(A) = 0.5$, $P(B) = 0.3$. If they are mutually exclusive, what is the probability that neither $A$ nor $B$ occurs?

Three events $A, B$ and $C$ are such that $P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A \cap B) = 0.08, P(A \cap C) = 0.28, P(B \cap C) = 0.2$. Find the minimum possible value of $P(A \cap B \cap C)$.

Let $A$ and $B$ be two events such that $P(A \cup B) = 0.7$ and $P(A) = 0.4$. Find $P(B)$ if $A$ and $B$ are mutually exclusive.

If $P(A) = 0.3, P(B) = 0.2, P(C) = 0.1$ and $A, B, C$ are mutually exclusive events, find $P(A' \cap B' \cap C')$.

A coin and a die are thrown simultaneously. What is the total number of outcomes in the sample space?

If $P(A) = 0.8$ and $P(B) = 0.5$, and $P(A \cap B) = 0.4$, find the probability that exactly one of the events $A$ or $B$ occurs.

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

In a deck of 52 cards, how many cards are 'not an Ace'?

If $P(A) = 0.3$ and $P(B) = 0.6$, what is the maximum value of $P(A \cap B)$?

If $P(A) = 0.5$, $P(B) = 0.4$, and $P(A \cup B) = 0.8$, then $P(A \cap B)$ is:

Given $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cup B) = 0.6$, find $P(A' \cup B')$.

If the odds in favor of an event are $5:4$, what is the probability of the non-occurrence of that event?

The probability that a student passes in Mathematics is $4/9$ and in Physics is $2/5$. If the probability of passing in at least one of them is $4/5$, what is the probability of passing in both?

Two dice are thrown. What is the probability that the sum of numbers is neither 7 nor 11?

Given $P(A) = 0.5$ and $P(B) = 0.4$, if $A$ and $B$ are mutually exclusive, $P(A \cap B)$ is:

If $P(A) = 0.6$, $P(B) = 0.3$, and $A$ and $B$ are mutually exclusive, find $P(A' \cup B')$.

In a deck of 52 cards, the event 'Picking a Red card' and 'Picking a Club' are:

If the probability of occurrence of event $A$ is $\frac{1}{2}$ and event $B$ is $\frac{1}{4}$, and they are mutually exclusive, find the probability of occurrence of neither $A$ nor $B$.

For two mutually exclusive events $A$ and $B$, it is given that $P(A) = \frac{1}{2} P(B')$ and $P(A \cup B) = \frac{5}{6}$. Find the value of $P(A)$.

If $A, B$ are mutually exclusive, $P(A) = 0.45, P(B) = 0.35$, find $P(A \cup B)'$.

Events $A$ and $B$ are mutually exclusive. Given $P(A) = p$ and $P(B) = q$, find $P(A \cap B)$.

If $A, B, C$ are three mutually exclusive and exhaustive events such that $P(A) = p, P(B) = q, P(C) = r$, which of the following is always true?

Let $A$ and $B$ be mutually exclusive events. If $P(A) = 0.2$ and $P(B) = 0.3$, find $P(A \cup B')$.

If $P(A) = p$ and $P(B) = 1-p$ are mutually exclusive, then $P(A \cup B)$ is:

Which of the following describes exhaustive events $A$ and $B$?

The union of all elementary events of a sample space $S$ is:

If $A$ and $B$ are mutually exclusive and exhaustive, then $P(B)$ is equal to:

If $S = \{1, 2, 3\}$, which of the following is an exhaustive set of events?

If $A, B$ are exhaustive events with $P(A) = 0.6$ and $P(B) = 0.6$, what is the probability that exactly one of the events $A$ or $B$ occurs?

Suppose $S = \{1, 2, 3, 4\}$. If $E_1 = \{1, 2, 3\}$ and $E_2 = \{2, 3, 4\}$, then $E_1$ and $E_2$ are:

If $A$ and $B$ are exhaustive events such that $P(A) = 0.6$ and $P(B) = 0.4$, find $P(A \cap B)$.

If $A, B, C$ are exhaustive events and $P(A \cap B) = P(B \cap C) = P(C \cap A) = 0$, then $P(A) + P(B) + P(C)$ is equal to:

If $A$ and $B$ are exhaustive events and $P(A) = 3/5$, then $P(B)$ cannot be less than:

Three events $A, B, C$ are exhaustive. If $P(A) = 0.6$ and $P(B) = 0.7$, what is the maximum possible value of $P(C)$?

A wheel is divided into $8$ equal sectors numbered $1$ to $8$. What is the probability that the spinner lands on an odd number?

Two dice are thrown. What is the probability that the sum of numbers is greater than $10$?

The sum of the probabilities of all elementary events of an experiment is always equal to:

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

The letters of the word 'MATHEMATICS' are arranged at random. What is the probability that the two M's are together?

If 2 balls are drawn from a bag containing 3 white, 4 black, and 5 red balls, what is the probability that both are of the same color?

A single card is drawn from a pack of 52 cards. What is the probability that the card is either a red card or a king?

Five people are chosen from a group of 8 men and 4 women. What is the probability that the group contains exactly 2 women?

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, what is the probability that more blue balls are drawn than red balls?

An urn contains 5 red, 6 white, and 7 black balls. Two balls are drawn at random. What is the probability that they are of different colors?

Given $P(A) = 0.3, P(B) = 0.4$, and $P(A \cup B) = 0.5$, find $P(A \cap B)$.

If $P(A) = 0.4, P(B) = 0.5$, and $P(A \cap B) = 0.2$, calculate $P(A \cup B)$.

A card is drawn from a 52-card deck. What is the probability that it is a 10 or a Heart?

The probability of an event $A$ is $2/3$ and event $B$ is $1/6$. If $A$ and $B$ are mutually exclusive, find $P(A \text{ or } B)$.