🎲 probability

1. **State the problem:** We have a lottery machine that outputs digits 0 through 9 with equal probability if fair. We tested it 200 times and recorded the frequency of each digit.

1. **State the problem:** We have a spinner divided into 5 equal sectors: Red, Blue, Yellow, Blue, Yellow. 2. **Formula for probability:** The probability of landing on a particula

1. **State the problem:** We have a spinner divided into 5 equal sectors: Red, Blue, Yellow, Blue, Yellow. 2. **Find the probability of landing on red:** Since all sectors are equa

1. The problem is to express the number of sectors labeled A as a ratio compared to the total number of sectors on the spinner. 2. The spinner is divided into 12 equal sectors with

1. The problem asks for the total number of sectors on a wheel/spinner. 2. The wheel is divided into 10 equal sectors labeled A, B, and C.

1. **State the problem:** We have a dartboard with 5 equal slices numbered 1 to 5. - Slices 2, 3, and 4 are grey.

1. **State the problem:** We have 8 balls numbered 1 to 8. Balls 1, 2, and 6 are grey (not white), and balls 3, 4, 5, 7, and 8 are white. We want to find the probabilities of selec

1. **State the problem:** We have a rectangular board of dimensions 30 ft by 20 ft, with two circles inside it. The small circle has a diameter of 6 ft, and the large circle has a

1. **State the problem:** We have two sets of homework problems chosen by students: - $X$: problems 1 to 7 (application problems)

1. **State the problem:** Given probabilities $P(A \cup B) = 0.84$, $P(A \cap B) = 0.12$, and $P(A) = 0.60$, find $P(B)$. 2. **Formula used:** The formula for the union of two even

1. Énoncé du problème : Calculer la variance de la variable aléatoire $Z$ dont la loi de probabilité est donnée par : | Valeur $k$ de $Z$ | $-5$ | $0$ | $10$ |

1. **Stating the problem:** Mark travels by train or bus.

1. **Problem statement:** You roll a fair six-sided die twice. Calculate the probabilities for the following events: a) Event A: Rolling the number 6 twice.

1. **State the problem:** Colton has a 5% chance of popping a silver balloon each throw. He throws 6 darts. We want to find the probability that he pops at least 1 silver balloon.

1. **State the problem:** We want to find the probability that at least 7 out of 8 sunflowers grow to be six feet tall based on Chad's simulation results.

1. **Problem:** Find $P(\text{even} \mid \text{at least } 12)$ when a number from 1 to 40 is chosen at random. 2. **Step 1: Define the conditional probability formula:**

1. **State the problem:** We are given two independent events A and B with probabilities $P(A) = 0.82$ and $P(B) = 0.60$. We need to find the probability of both events occurring t

1. **Problem statement:** Calculate the probability that in 80 independent roulette spins, the ball lands on a specific number at least 4 times.

1. Problem 15: Given the probability distribution of $X$: $$\begin{array}{c|ccccccc}

1. **Problem statement:** Find the expected value and variance of the random variable $X$ defined as the sum of faces when a pair of dice is thrown. 2. **Formula and rules:**

1. **Problem Statement:** We have a random variable $X$ defined as the sum of the faces when a pair of dice is thrown. We need to find the expected value $E(X)$ and variance $Var(X