Probability

Out of $50$ cars that passed a gate, $12$ were red. What is the experimental probability that the next car is NOT red?

A card is picked from a standard deck. What is the probability it is either a Red card or a Black card?

A bag has $10$ Red, $5$ Green, and $5$ Blue items. What is the probability of selecting a Green item?

If a month is chosen at random, what is the probability that its name ends with the letter 'y'?

A box contains $5$ yellow, $3$ red, and $2$ blue balls. What is the probability of selecting either a yellow or a blue ball at random?

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is $4$ or less?

A bag contains $10$ red and $8$ blue marbles. If two marbles are chosen at random without replacement, what is the probability that at least one is red?

From a group of 3 men and 3 women, 3 people are selected at random. What is the probability that the group contains exactly 1 man and 2 women?

A bag contains $n$ counters. One is red and the rest are blue. Two counters are taken at random without replacement. The probability that they are both blue is $0.8$. Find $n$.

In a factory, Machine A produces $60\%$ of the items and Machine B produces $40\%$. $2\%$ of Machine A's items are defective and $3\%$ of Machine B's items are defective. If a randomly selected item is defective, what is the probability it came from Machine B?

Two spinners each have two sections numbered 1 and 2. If both are spun, what is the probability that the sum of the numbers is 3?

If $P(A) = 0.2$ and $P(B) = 0.3$, what is $P(A \text{ and } B)$ given that the events are independent?

A fair six-sided die is rolled. What is the probability of rolling a 6 and then rolling another 6?

A spinner has two equal sections: Red and Blue. A coin is tossed. What is the probability of getting 'Red' and 'Tails'?

In a certain town, $70\%$ of people support the local sports team. If three people are chosen at random, what is the probability that all three support the team?

A box contains 8 white and 4 red balls. Two balls are drawn without replacement. What is the probability that both are white?

Two fair six-sided dice are rolled. What is the probability that the sum of the numbers is a prime number?

In a game of 'Best of 3', player A has a probability $0.6$ of winning any single game. What is the probability that A wins the match (wins 2 games before B wins 2)?

A computer generates two digits from 0-9. What is the probability that at least one digit is a prime number? (Primes: 2, 3, 5, 7)

A bag has 6 red and $n$ blue balls. Two balls are drawn without replacement. The probability that they are the same color is $\frac{3}{5}$. Find $n$.

In a group of 10 students, 6 study Art ($A$), 4 study Music ($M$), and 2 study both. What is the probability that a student studies Music but NOT Art?

Given $P(A \cup B) = 1$, which of the following must be true?

In a Venn diagram, $n(A) = 18$ and $n(A \cap B) = 6$. What is the number of elements in the region 'A only'?

If $n(\xi) = 40$, $n(A) = 20$, and $n(B) = 15$, and $n(A \cap B) = 0$, what is $P(A \cup B)'$?

If $P(A) = 0.25$, $P(B) = 0.45$, and $P(A \cup B) = 0.55$, find $P(A \cap B)$.

Given $n(\xi)=100$, $n(A \cap B)=20$, and $n(A)=50$, find the probability $P(B'|A)$.

In a Venn diagram, the shaded region represents $A' \cap B$. If $P(A' \cap B) = 0.35$ and $P(B') = 0.4$, find $P(A \cap B)$.

In a group, $P(A) = 0.6$ and $P(B) = 0.3$. If $A$ and $B$ are mutually exclusive, find $P(A' \cap B')$.

If $n(A) = 25$, $n(B) = 30$, $n(A \cap B) = 12$, and $n(A \cup B)' = 7$, find the total number of elements in the universal set $\xi$.

In a collection of 50 coins, 20 are silver ($S$), 15 are rare ($R$), and 5 are both silver and rare. If a coin is not silver, find the probability it is rare.

A basket contains 5 pears and 5 apples. A fruit is picked and not replaced. If the first fruit picked was a pear, what is the probability the second is an apple?

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

Counters numbered 1 to 10 are in a bag. Given that a counter drawn is odd, what is the probability that it is a prime number?

A card is drawn from a standard deck. Given that it is a Spade, what is the probability it is the Ace of Spades?

Three fair coins are tossed. Given that at least two of the coins show Heads, what is the probability that all three coins show Heads?

A disc is drawn from a bag containing 10 discs numbered 1 to 10. What is the probability that the number is a multiple of 3, given that it is an even number?

If $P(X \cap Y) = 0.2$, $P(X \cup Y) = 0.9$, and $P(X) = 0.5$, find $P(X|Y)$.

A bag contains 4 red and 2 white balls. A ball is drawn and its color noted. It is not replaced, but a ball of the other color is added to the bag. A second ball is then drawn. Given the second ball is red, what is the probability the first ball was red?

In a large group, $70\%$ are adults and $30\%$ are children. $80\%$ of adults like swimming, while $60\%$ of children like swimming. If a person is chosen and they like swimming, what is the probability they are an adult?

A student answers a multiple-choice question with 4 options. The probability the student knows the answer is $0.6$. If they don't know, they guess with a $1/4$ chance of being correct. Given they got it right, what is the probability they actually knew the answer?

1. Relative and Expected Frequencies: practice question 1 for Probability?

1. Relative and Expected Frequencies: practice question 2 for Probability?

1. Relative and Expected Frequencies: practice question 3 for Probability?

1. Relative and Expected Frequencies: practice question 4 for Probability?

1. Relative and Expected Frequencies: practice question 5 for Probability?

1. Relative and Expected Frequencies: practice question 6 for Probability?

1. Relative and Expected Frequencies: practice question 7 for Probability?

1. Relative and Expected Frequencies: practice question 8 for Probability?

1. Relative and Expected Frequencies: practice question 9 for Probability?

1. Relative and Expected Frequencies: practice question 10 for Probability?