🎲 probability

1. **State the problem:** We have a bag with 2 red marbles and 3 blue marbles, total 5 marbles. We want to find the probability of drawing 2 red marbles when drawing 2 marbles with

1. **State the problem:** We are given probabilities related to rain and flight delays at LaGuardia Airport. We want to find the probability that it is raining given that the fligh

1. **Problem statement:** We are given a binomial distribution $X \sim b(15, 0.4)$ and asked to find $P(X=7)$. 2. **Formula:** The binomial probability formula is

1. **Stating the problem:** Two fair six-sided dice are rolled, and the numbers on the two dice are added together to give a score. We need to find the most likely score. 2. **Form

1. **Problem statement:** Aoibhín guesses answers to 20 multiple-choice questions, each with 4 options and only 1 correct. We find probabilities for getting none, exactly five, and

1. **Problem statement:** A bag contains 5 red, 4 blue, and 6 white marbles (total 15). Marbles are drawn without replacement. Find probabilities for various events. 2. **(i) Proba

1. **Problem Statement:** Two standard dice are rolled. A. What is the probability that you roll doubles 3 times in a row?

1. **Problem Statement:** Two standard dice are rolled. Find the probability that you roll doubles 3 times in a row. 2. **Formula and Rules:** The probability of rolling doubles on

1. **Problem:** Find $P(\text{yellow, then red})$ when choosing markers with replacement. 2. **Formula:** For independent events with replacement, $P(A \text{ then } B) = P(A) \tim

1. **State the problem:** We have a spinner with 10 equal regions: 3 red, 4 blue, 2 yellow, and 1 green.

1. **State the problem:** We have a spinner with 10 equal regions: 3 red, 4 blue, 2 yellow, and 1 green. 2. **Define the winnings:**

1. **State the problem:** Calculate the expected value of the spinner game where the wheel has 10 equal regions: 3 red, 4 blue, 2 yellow, and 1 green.

1. **State the problem:** Calculate the expected value of the winnings from a spinner with 10 equal regions: 3 red, 4 blue, 2 yellow, and 1 green.

1. **State the problem:** We have a game where a player rolls a die. If the die shows 6, the player wins 40. Otherwise, the player wins 0. The cost to play is 8. We want to find th

1. **State the problem:** We have a game where a player rolls a fair six-sided die.

1. **State the problem:** We have a game where an eight-sided die (values 1 to 8) is rolled.

1. **State the problem:** Calculate the probabilities of reaching each final outcome in a branching tree diagram with given branch probabilities.

1. **Stating the problem:** We have a branching probability tree with nodes A and B and various transition probabilities along the branches.

1. **State the problem:** Calculate the expected value of a game where a card is drawn from a standard 52-card deck.

1. **State the problem:** We want to find the probability that a randomly selected person is a young adult given that they own a cat. 2. **Recall the formula for conditional probab

1. **State the problem:** We need to find the expected value of the winnings from a game with given payout probabilities. 2. **Formula:** The expected value $E(X)$ of a discrete ra