🎲 probability

1. **Problem Statement:** A bag contains six balls labeled 1 through 6. One ball is randomly picked. We need to find the probability of picking a ball labeled with a multiple of 3.

1. **State the problem:** We have a bag with eight tiles labeled F, G, H, I, J, K, L, and M. We want to find the probability of picking a vowel. 2. **Identify vowels:** The vowels

1. **Problem statement:** We have a six-sided die with sides labeled 1 through 6. We want to find the probability of rolling a number greater than 2. 2. **Formula for probability:*

1. **Problem 11 (a):** Three students A, B, and C throw a tetrahedral die in order. The first to throw a 4 wins. The game continues indefinitely until someone wins. Find the probab

1. **Problem Statement:** Yuri has four sets of cards (A, B, C, D) with different numbers on them. He chooses one set and picks a card from it 600 times with replacement. He gets t

1. **Problem statement:** Mia writes down five whole numbers and picks one at random. Outcome E is picking an even number, and outcome O is picking an odd number. We need to determ

1. **Problem Statement:** We have two problems involving probability based on frequency tables.

1. **Problem:** Find the probability that a randomly chosen fisherman was fishing far from shore and caught bangus. 2. **Formula:** Probability of an event = \( \frac{\text{Number

1. The problem is to understand and solve a question involving a tree diagram. 2. A tree diagram is a graphical representation used to list all possible outcomes of an event or ser

1. Let's explore a random problem involving a tree diagram. 2. Problem: Suppose you have a bag with 3 red balls and 2 blue balls. You draw two balls one after the other without rep

1. Problem: Find the probability that all three children are boys if a couple has three children. Formula: Probability of all boys = $\left(\frac{1}{2}\right)^3$ since each child c

1. **Problem statement:** There are 8 students who prefer maths (M) and 3 who prefer English (E). The teacher calls on two students with replacement. We want to find the probabilit

1. Problem: Given three boxes with capacitors of different values, find probabilities related to selecting capacitors. 2. For i) Probability of selecting a 0.01-μF capacitor given

1. **Problem Statement:** We are given probabilities related to a person's travel choices: fractions 2/9, 1/9, 2/5, and 3/7. We need to understand the concepts of certain and impos

1. **Problem statement:** We have two independent random variables $Y_1$ and $Y_2$ with probability density functions (pdfs) $$f_1(y_1) = 6y_1(1 - y_1), \quad 0 \leq y_1 \leq 1$$

1. **Problem Statement:** The number of cars arriving at the station in an hour follows a Poisson distribution with an average rate $\lambda = 5$ cars per hour.

1. **Problem statement:** A gardener planted 20 tomato seeds with a 50% chance each seed will germinate. 2. **Relevant formula:** This is a binomial probability problem where the n

1. The problem involves understanding the probabilities of an event $X$ and its complement $\text{not } X$. 2. By definition, the probability of an event $X$ is denoted as $P(X)$,

1. **Stating the problem:** We have a coin flip (2 outcomes: heads or tails) and a roll of a number cube (6 outcomes: numbers 1 through 6). We want to find:

1. **State the problem:** We have 11 students in Ms. Gray's class with memberships in Art Club (A) and Dance Club (B). We want to find various probabilities related to these events

1. **Problem Statement:** We have 14 students in Ms. Evans's class. The Tennis Club members are Felipe, Leila, Eric, Hong, Debra, Raina, Christine, Aldo, Rachel (9 total including