🎲 probability

1. **Problem Statement:** In a group of five potential blood donors—a, b, c, d, and e—only a and b have type O-positive blood. Five blood samples, one from each individual, will be

1. **Problem statement:** (a) Given $P(A) = 0.9$ and $P(L) = 0.45$, find the probability that a worker with a laptop is connected to router A.

1. **Problem Statement:** Find the probability of winning a prize in a lottery where there are 10 prizes and 30 blanks. 2. **Formula:** Probability of an event $E$ is given by

1. **Problem statement:** We want to find the probability that exactly 5 out of 10 randomly chosen students prefer red shirts. 2. **Assumptions and formula:** We assume each studen

1. **Problem Statement:** We are given the function $$f(x) = 1 - \left(1 - \frac{x}{102}\right)^{\frac{1}{6}}$$ defined for $$0 \leq x \leq 120$$. We want to find the probability t

1. **Problem Statement:** Thilina randomly selects one card from 7 cards numbered 1 to 7.

1. **Problem Statement:** Find the moment generating function (MGF) $M_X(s)$ and all moments $E[X^k]$ of a random variable $X$ with exponential distribution parameter $\lambda$, wh

1. **State the problem:** We are given a probability distribution table for a discrete random variable $X$ with values $0,1,2,3,4,5,>5$ and corresponding probabilities $0.54,0.26,0

1. **Problem Statement:** We have two probability distributions for the number of aces served by Michelle and Amanda in each tennis set. We need to find the expected value (mean),

1. **Stating the problem:** We have a probability distribution with values $x_i = 2, 4, 10, 20$ and corresponding probabilities $p_i = k, 0.05, 0.35, 3k$. We need to find: a) The v

1. **State the problem:** We are given the probabilities that Kebba, Ebou, and Omar will hit a target as $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{4}{5}$ respectively. We need to fi

1. **Problem 1:** A delegation of 3 is selected from a city council of 5 liberals and 4 conservatives. Let $X$ be the number of liberals selected. 2. **Problem 2:** In a club with

1. **Problem Statement:** A family has five children. The random variable $x$ represents the number of boys in the family. We want to find: (a) The expected value $E(x)$ of $x$.

1. **Problem 1: Discrete Probability Distribution** Given the probabilities for $X$ with values $0,1,2,3,4,5$ and probabilities $0.05,0.1,0.2,0.3,k,0.15$ respectively.

1. **Stating the problem:** Amoatemaa is deciding which courses to take. Given probabilities:

1. **State the problem:** We have a bag with red and blue counters in the ratio 4 : 10. 2. **What is asked:** Find the probability that a randomly chosen counter is blue.

1. **Problem 1: Given the joint probability distribution of X and Y as** $$\begin{array}{c|ccc}

1. **Stating the problem:** We have a probability table for the outcomes of a game: win, lose, and draw. The probabilities for win and lose are given as 0.3 and 0.25 respectively,

1. **Problem 1: Lottery Tickets** We have 5000 tickets sold at 1 each.

1. **State the problem:** We have three bags A, B, and C with red and white counters. Ratios and counts are given, and counters are moved between bags. We want the probability that

1. **Problem:** Find the theoretical probability of selecting a number from the sample space \{2, 3, 4, 5\}. Theoretical probability formula: $$P(E) = \frac{\text{Number of favorab