🎲 probability

1. **State the problem:** A box contains 4 chocolates and 1 fruit chew. Clark and Chloe take turns drawing a treat without replacement. Clark draws first. The one who draws the fru

1. The problem involves calculating the probability that Chloe wins a game where draws are made from a set of candies including 1 Fruit Chew and 4 chocolates. 2. The first event is

1. **Problem statement:** We have a web application generating passwords where 15% are rejected for being too weak. We want to find probabilities and statistics related to the numb

1. **State the problem:** We have a probability distribution for the number of customers $X$ who order takeout in a day with probabilities involving $k$. We need to find $k$, then

1. **State the problem:** Find the constant $k$ for the probability density function (pdf) of the random variable $Z$ given by

1. **Problem:** Find the probability of rolling a number greater than 4 on a fair six-sided die. 2. **Formula:** Probability of an event $E$ is given by

1. **Problem statement:** We have a group of students consisting of 3 freshmen, 10 sophomores, 5 juniors, and 6 seniors. We want to find the probability of choosing exactly 3 senio

1. **State the problem:** We want to find the probability of exactly 3 defective bulbs in a sample of 50, where each bulb has a 7% chance of being defective. 2. **Identify the dist

1. **Stating the problem:** We want to understand the Bernoulli distribution, which models a random experiment with exactly two possible outcomes: success or failure. 2. **Definiti

1. **Problem statement:** Given Angela picks two numbers, one from \{1,2,3\} and one from \{4,5,6\}, and their sum is odd, find the probability that one of the numbers is 3. 2. **U

1. সমস্যাটি হলো: একটি র‍্যান্ডম ভেরিয়েবল $X$ এর প্রোবাবিলিটি ডিস্ট্রিবিউশন দেওয়া আছে: $$f(x) = \frac{x+1}{8}, \quad x = 0, 2, 3$$

1. **Problem 1:** Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls. Let $V$ be the random variable representing the nu

1. **Problem statement:** Find the probability that

1. **Problem statement:** Find the probability that (i) only one of Mutola or Murumbi is selected, and (ii) none of them is selected, given:

1. **State the problem:** We need to find the experimental probability of hitting the sector numbered "8" on a circular target after 120 throws, where the dart hits sector 8 exactl

1. The problem is to understand the Binomial Distribution. 2. The Binomial Distribution models the number of successes in a fixed number of independent trials, each with the same p

1. **Problem statement:** We have a random variable $T$ representing time, and a score $P = a - bT$ where $a,b > 0$. Given $E(P) = 100$, maximum score $= 150$, $E(T) = 4.723$, and

1. **Problem statement:** We are given a piecewise probability density function (pdf) for the time $T$ taken by runners to complete a marathon, defined on $[2.25,7.5]$ hours. We ne

1. **Problem:** A bowl contains 10 chips numbered 1 to 10. Find the probability of drawing a chip with certain properties. 2. **Formula:** Probability of an event $E$ is given by

1. Problem: Find the probability of rolling a 3 twice on a number cube. Formula: Probability of independent events both occurring is $$P(A \text{ and } B) = P(A) \times P(B)$$.

1. **Problem:** Find the probability of rolling a 3 twice on a number cube. 2. **Formula:** The probability of independent events both occurring is the product of their individual