🎲 probability

1. **Problem Statement:** Given a binomial random variable $X \sim B(8, 0.2)$, calculate various probabilities. 2. **Formula:** The binomial probability mass function is

1. **Problem statement:** We have a deck with two cards each of the integers from -10 to 10, excluding zero. We want the probability of dealing two cards whose product is 12. 2. **

1. **Stating the problem:** We want to find the probability that at least 5 accidents occur in a given month at an intersection. 2. **Understanding the problem:** "At least 5 accid

1. **Problem statement:** On average, 3 traffic accidents per month occur at a certain intersection. We want to find the probability that fewer than 6 accidents occur in any given

1. **State the problem:** Carly has picked some pieces of train track: 8 straight, 7 curved, 4 cross, and 5 switch tracks. We want to find the probability that the next piece she p

1. **State the problem:** We are given the probabilities of a student having ginger hair and blonde hair, and we need to find the probability that a student has either ginger or bl

1. The problem asks for the probability that exactly one new visitor arrives at a website in any given hour. 2. This is a classic Poisson distribution problem where the number of e

1. **Problem statement:** We are given that the number of new visitors to a website in one hour follows a Poisson distribution with mean $\lambda = 2.8$. We want to find the probab

1. The problem is to find the probability that a person has the disease given a positive test result, using the sensitivity, specificity, and prevalence. 2. We use Bayes' theorem:

1. **Problem statement:** We need to color a spinner (Glücksrad) divided into 12 equal segments according to the given probabilities: - $P(\text{orange}) = \frac{1}{3}$

1. **Problem:** Find the probability that a student from the sample receives an allowance. 2. **Given Data:**

1. **State the problem:** Determine if events V (Took a vacation) and C (Have cable TV) are independent. 2. **Recall the definition of independence:** Two events V and C are indepe

1. **State the problem:** Marco designed a spinner wheel with 4 equal sections (red, blue, green, yellow), each supposed to have a 25% chance of landing. 2. **Expected outcomes:**

1. **Problem statement:** 100 students were surveyed about enjoying running (R), cycling (C), or swimming (S). We are given counts for each region in the Venn diagram and asked to

1. **Problem:** Sketch a graph of the uniform probability distribution of $X$, where $X$ is the time in minutes from when the alarm is set to when it goes off, uniformly distribute

1. **State the problem:** We have 11 pens: 8 black and 3 red. Two pens are drawn without replacement. We want the probability that both pens are the same color. 2. **Formula for pr

1. **State the problem:** We need to find the probability of getting an even number on the spinner and the color green on the dice. 2. **Identify probabilities from the problem:**

1. **State the problem:** We have 80 students attending revision lessons in History, Computing, or Geography on Saturday or Sunday. 2. **Given data:**

1. **State the problem:** We are given conditional probabilities of rain on consecutive days and the probability of rain on Monday. We need to estimate the probability of rain on W

1. **State the problem:** We need to find the probability that a randomly chosen Year 13 student cycles to college. 2. **Identify the relevant data:** From the table, the number of

1. **State the problem:** We have 100 pupils surveyed at a sports centre. They can use either the swimming pool (S), the gym (G), or neither. Given: