🎲 probability

1. **State the problem:** We want to find the probability that a student rides the bus given that they are a senior. 2. **Recall the formula for conditional probability:**

1. **State the problem:** We want to find the probability that a randomly chosen customer purchased either popcorn or a hamburger. 2. **Identify the data:** From the table, the pur

1. **State the problem:** We toss two six-sided dice. Event A: The first die lands on 1 or 2.

1. **Problem statement:** Calculate the probability that Anna wins two main prizes when she buys 2 tickets from 100 tickets, where 3 are main prizes and 12 are consolation prizes.

1. **State the problem:** We have a sample space $S = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$, event $F = \{2, 3, 4, 5, 6\}$, and event $G = \{6, 7, 8, 9\}$. We want to list th

1. **State the problem:** We have a sample space $S = \{2,3,4,5,6,7,8,9,10,11,12,13\}$. 2. **Define the events:**

1. **State the problem:** We want to find the probability that a randomly chosen candy is either red or has no smile. 2. **Identify given probabilities:** From the table:

1. **Problem statement:** Given a random variable $X$ with values and probabilities: | $x$ | 0 | 10 | 20 | 30 |

1. **Problem Statement:** We have a binary code word of length 6 bits, each bit is either 0 or 1. We want to find the probabilities for three cases:

1. **State the problem:** We are given probabilities of plots having pairs and all three types of trees: cedar, cypress, and redwood. We want to find the probability that a randoml

1. **State the problem:** We are given the probabilities of intersections of three types of trees (Cedar, Cypress, Redwood) in quarter-acre plots. 2. **Given data:**

1. **State the problem:** We need to find the percentage of applicants admitted to the college. Admission requires either a GPA of at least 3.0 or an SAT score of at least 1200. 2.

1. **State the problem:** We have a box with 3 red balls and 5 blue balls. We draw 3 balls one by one with replacement, and we want to define the sample space for the colors record

1. The problem asks for the probability of tossing two heads and one tail in three coin tosses. 2. The formula for probability is $P(E) = \frac{\text{Number of favorable outcomes}}

1. **State the problem:** We want to find the experimental probability of tossing two heads and one tail in any order based on the given simulation data. 2. **Identify outcomes wit

1. **State the problem:** We want to find the probability of randomly choosing a lunch with Tacos and Chips. 2. **Identify total possible lunches:** Each lunch consists of one Entr

1. Let's start by stating the problem: Probability measures how likely an event is to happen. 2. The formula for probability of an event $E$ is given by:

1. **State the problem:** We are given probabilities for paperback books, non-fiction books, and books that are both paperback and non-fiction. We need to find the probability of s

1. **Problem statement:** A special 10-faced die numbered 1 to 10 is rolled. We want to find the probability of landing on: (a) an even number

1. **State the problem:** We have a probability density function (PDF) defined as $$f(x) = \begin{cases} 6.22 e^{-x^{6.22}} x^{5.22}, & x \geq 0 \\ 0, & x < 0 \end{cases}$$

1. **Stating the problem:** A die is thrown once. We want to find the probability of three events: (a) The score is greater than 3.