🎲 probability

1. **Problem Statement:** We need to formulate a probability mass function (PMF) for the number of days Ingrid takes the yellow bus to school over three consecutive days. 2. **Unde

1. The problem is to evaluate the function $f(x) = \frac{\binom{4}{x}}{16}$ for $x = 0, 1, 2, 3, 4$ and understand its values. 2. The binomial coefficient $\binom{n}{k}$ represents

1. **Problem Statement:** We have two unbiased dice with random variables $X$ and $Y$ representing the numbers on each die. We want to find the probability mass functions (PMFs) of

1. **State the problem:** We want to find the probability of getting no prime numbers when two dice are thrown. 2. **Identify prime numbers on a die:** The numbers on a die are 1,

1. **Stating the problem:** We are given that the probability it will rain on any day is $\frac{1}{6}$. We need to find:

1. **Problem Statement:** We have a uniform distribution for the average number of donuts eaten by a nine-year-old child per month, ranging from 1 to 6 donuts inclusive.

1. **Problem Statement:** A random variable $X$ has a probability distribution given by

1. **Problem Statement:** Calculate the marginal probabilities from the joint probability table for events $A_1, A_2, A_3$ and $B_1, B_2$. 2. **Given Joint Probabilities:**

1. The problem asks to fill in a 3x4 table showing the outcome, probability, and payout. 2. To solve this, we need to understand what the outcomes are, their probabilities, and the

1. **Problem Statement:** You pay 1 to play a game where two fair dice are rolled. You win 3 if the sum is 6, 7, or 8; you win 5 if the sum is 2 or 12; otherwise, you lose your 1.

1. **State the problem:** We have a probability distribution for items sold by the Booster Club with some probabilities given and one missing. We need to find the missing probabili

1. **State the problem:** We have a discrete random variable $X$ representing the number of patients visiting a clinic each day with probabilities: $$P(0) = 0.2, \quad P(1) = 0.3,

1. **State the problem:** We need to find the probability that Miss Robinson does not win the raffle. 2. **Given information:**

1. **Stating the problem:** We have a bag with counters of four colors: pink, yellow, green, and blue. The probabilities of drawing each color are given as pink 0.5, yellow 0.2, gr

1. **Stating the problem:** We have a bag containing counters of four colors: pink, yellow, green, and blue. We want to understand the probabilities of randomly drawing each color

1. **Stating the problem:** We have a bag with counters of four colors: pink, yellow, green, and blue. We want to understand the probabilities of drawing each color at random from

1. **Problem statement:** There are red and blue counters in a bag with a ratio of red to blue counters as 3:1. Two counters are removed at random, and the probability that both ar

1. **הבעיה:** להוכיח כי עבור משתנים מקריים X,Y עם מומנטים שניים סופיים, ופונקציה הפיכה $g:\mathbb{R} \to \mathbb{R}$ מתקיים: $$E[X|g(Y)] = E[X|Y]$$

1. **Problem statement:** A meeting has 4 Americans and 2 Germans. Three consuls are selected at random. We want to find the probability distribution of the random variable $G$, wh

1. **Problem statement:** A bag contains five marbles: 1 blue (B), 1 red (R), and 3 green (G). Two marbles are selected without replacement. We need to list all possible outcomes u

1. **Problem Statement:** Illustrate the sample space using a tree diagram for the orderings in which 3 girls Sarah, Tracy, and Beth may sit in a row of 3 chairs.