🎲 probability

1. The problem is to find the probability of events 4 and 5 using the complementary events formula. 2. The complementary events formula states that $P(A) = 1 - P(A^c)$, where $A^c$

1. **Problem 4a:** Find the complement probability $P(A^c)$ given $P(A) = 0.0175$. The complement rule states:

1. **Problem Statement:** We want to find the probability of getting a sum of 6 when two dice are rolled. 2. **Formula:** Probability is given by the ratio of favorable outcomes to

1. **Problem statement:** We have events:

1. The problem asks: What is a random variable? 2. A random variable is a function that assigns a numerical value to each outcome in a sample space of a random experiment.

1. **State the problem:** We are given a discrete random variable with values $x_i = 1, 3, 7, 8$ and corresponding probabilities $p_i = 0.1, 0.4, p, 0.15$. We need to find the valu

1. **Problem:** (a) Given a Poisson random variable $X$ with $P\{X=0\} = e^{-\mu}$, find $E[X]$.

1. **Problem statement:** A box contains 6 discs: 4 blue and 2 red. Discs are drawn one by one without replacement. Let $X$ be the number of discs drawn up to and including the fir

1. **State the problem:** We want to find the probability that a customer tested Game A given that they recommended their game. This is a conditional probability problem. 2. **Reca

1. **Stating the problem:** We have a cumulative distribution function (CDF) $F:\mathbb{R} \to \mathbb{R}$ and a function $b:[0,1] \to \mathbb{R}$ defined by $$

1. **Problem statement:** A box contains 5 red, 3 blue, and 2 green marbles. Two marbles are drawn without replacement. Find the probability that exactly one red and one blue marbl

1. Let's clarify the problem: You want to know how to write the possible outcomes correctly, which usually refers to listing all possible results of an experiment or event. 2. The

1. **State the problem:** We want to find the probability that a customer shops online given that the customer is female. 2. **Formula used:** The conditional probability formula i

1. **State the problem:** We are given the probabilities of passing two exams: Statistics ($P(S) = 0.7$) and Math ($P(M) = 0.9$), and the probability of passing both exams ($P(S \c

1. **Stating the problem:** We are given a discrete random variable with scores and their corresponding probabilities. We need to find the expected value (mean) and the standard de

1. **State the problem:** We are given a discrete random variable with scores and their corresponding probabilities. We need to find the expected value (mean) and the standard devi

1. **Problem Statement:** Given the table of grades by gender, we need to find various probabilities related to the students. 2. **Total number of students:** $$74$$ (given in the

1. **Problem Statement:** We want to find the probability $P(X + Y \leq 5)$ for a continuous bivariate random variable $(X,Y)$ with joint density $g(x,y)$ defined over $0 < X < 4$

1. **Problem statement:** We want to find the correct integral expressions for the probability $P(X \leq 2 \cup Y \leq 2)$ where $(X,Y)$ is a continuous bivariate random variable w

1. **Problem Statement:** You start with 3 tokens and want to reach 5 tokens before hitting 0. Each turn, you bet the maximum tokens possible but not more than needed to reach 5 if

1. **State the problem:** You roll three fair 6-sided dice. The payouts are: - $20 if all three dice show the same number.