🎲 probability

1. **State the problem:** We want to find the theoretical probability of drawing a king from a standard 52-card deck. 2. **Formula for theoretical probability:**

1. **State the problem:** We want to find the experimental probability of landing on B after spinning the wheel 78 times and landing on B 21 times. 2. **Formula for experimental pr

1. **State the problem:** We need to find the fraction of times the spinner lands on either blue or yellow. 2. **Identify the fractions:** The spinner lands on blue with probabilit

1. **Stating the problem:** Probability is the branch of mathematics that studies the likelihood of events occurring. 2. **Formula and rules:** The probability $P$ of an event $E$

1. **State the problem:** We have a spinner with numbers $1, 2, 3, 4, 5, 6, 7$ and we want to find the probability $P(\text{prime})$ that the spinner lands on a prime number. 2. **

1. **State the problem:** We have 8 cards numbered from $1$ to $8$. We want to find the probability that a randomly picked card is **not prime**. 2. **Identify prime numbers betwee

1. **State the problem:** Li has $t$ toy bricks consisting of red and blue bricks. We want to find $t$ given the probabilities of picking red bricks in two draws.

1. **State the problem:** We want to find the probability that a randomly chosen student is either female or received a grade of C. 2. **Identify the data from the contingency tabl

1. **State the problem:** We are given the inequality $$-6 \leq x \leq -3$$ and asked to find what $F_X$ equals. 2. **Understanding $F_X$:** Typically, $F_X$ denotes the cumulative

1. **State the problem:** We have customer counts by age groups and want to find probabilities for certain age ranges when one customer is chosen at random. 2. **Calculate total nu

1. **State the problem:** We want to find the probability that a randomly chosen athlete plays either football or basketball. 2. **Recall the formula for the union of two events:**

1. **State the problem:** We have joint density function $$f(x,y) = \frac{1}{3}x + \frac{1}{3}y$$ for $$0 \leq x \leq 2$$ and $$0 \leq y \leq 1$$, zero elsewhere. We want to find:

1. **State the problem:** We are given the cumulative distribution function (CDF) $F(x)$ of a discrete random variable $X$ representing the number of months between successive paym

1. **State the problem:** We are given seven over/under betting lines with odds for "over" and "under" outcomes. We need to calculate the sum of the reciprocals of each "over" and

1. **Problem:** Find the probability that a randomly selected respondent has been in a car accident. 2. **Formula:** Probability $P(E) = \frac{\text{Number of favorable outcomes}}{

1. **Problem 4:** Find the probability that "E" is drawn first and "F" is drawn second without replacement from 6 slips labeled A, B, C, D, E, F. 2. **Formula:** For events without

1. **State the problem:** We have a piecewise density function $$f(x) = 0.05$$ for $$0 < x \leq 5$$ and $$f(x) = 0.15$$ for $$5 < x \leq 10$$. We want to calculate the mean excess

1. The problem states that losses, denoted by $X$, follow a distribution with a probability density function (pdf). 2. To analyze or work with this distribution, we need the explic

1. **Problem statement:** We have 4 friends and 21 other boys, making a total of $4 + 21 = 25$ players. They are divided randomly into 5 teams of 5 players each. We want to find th

1. The problem is to solve a question using probability simply. 2. Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes.

1. **State the problem:** John has $6$ green marbles and $4$ purple marbles, total $6 + 4 = 10$ marbles.