🎲 probability

1. **Problem Statement:** Find the mean, variance, and standard deviation of the probability distribution for the number of heads $X$ when two coins are tossed. 2. **Given Data:**

1. **State the problem:** We have a population with values $0,0,5,7,8,9,9,10,12,14,15,16,18,19,19$ and a sample size of 14. We want to find the tree diagram of the probability of t

1. **Problem statement:** Find the probability that it will not rain next Friday and the probability that it will rain on exactly two Fridays out of three consecutive Fridays start

1. **Problem statement:** The probability it will rain on any day next week is half the probability it will rain on the same day this week; otherwise, it remains the same.

1. **State the problem:** We want to find the probability that Samuel chooses Rock in Game 1 and then Scissors in Game 2. 2. **Identify the probabilities from the tree diagram:**

1. **Problem Statement:** Define 'Conditional Probability' with a suitable example. 2. **Definition:** Conditional probability is the probability of an event occurring given that a

1. **State the problem:** We have counters in a bag with colors blue, silver, and green in the ratio 1 : 5 : 3. 2. **What is asked:** Find the probability that a randomly picked co

1. **Stating the problem:** We need to find 5 examples of mutually exclusive events where each event has a non-zero probability. 2. **Definition:** Mutually exclusive events are ev

1. **Problem:** Identify 5 examples of non-mutually exclusive events with explanations. 2. **Definition:** Non-mutually exclusive events are events that can occur at the same time,

1. **Problem Statement:** Identify 5 examples of non-mutually exclusive events and explain why they are non-mutually exclusive. 2. **Definition:** Non-mutually exclusive events are

1. **Problem:** Identify 5 examples of non-mutually exclusive events and explain why they are non-mutually exclusive. 2. **Definition:** Non-mutually exclusive events are events th

1. **Stating the problem:** We need to find 5 examples of mutually exclusive events where each event has a non-zero probability. 2. **Definition:** Mutually exclusive events are ev

1. **Problem:** Two events A and B are mutually exclusive if they cannot happen at the same time. 2. **Example 1:** Tossing a coin. Event A: Getting heads. Event B: Getting tails.

1. The problem states: A fair six-sided die is tossed. The player loses 5 pesos if the result is “1”, loses 5 pesos if the result is “6”, and wins 10 pesos for the other numbers (2

1. **Problem:** Two events A and B are mutually exclusive if they cannot happen at the same time. 2. **Definition:** Events A and B are mutually exclusive if $$P(A \cap B) = 0$$.

1. **State the problem:** We have a continuous random variable $X$ with probability density function (pdf) $$f(x) = k(2 - x)(2 + x), \quad 0 \leq x \leq 2.$$ We need to find:

1. **State the problem:** We are given a function $$f(x) = A(4x - 2x^2)$$ defined on the interval $$0 \leq x \leq 2$$. We need to find the value of $$A$$ such that $$f(x)$$ is a pr

1. **Problem Statement:** Given a discrete random variable $X$ with values $0,1,2,3,4,5$ and probabilities $0.05,0.10,0.15,0.30,0.25,0.15$ respectively, find:

1. **Problem statement:** We have a database with 100 records, 10 corrupted and 90 uncorrupted. A data analyst randomly selects 8 records. We want the probability distribution for

1. **Problem statement:** We have three network packets that can be routed to Link A, Link B, or Link C. Let $X$ be the number of packets routed to Link B. We want to find the prob

1. **Problem Statement:** We have a bag with 5 white tokens and 3 black tokens. Three tokens are drawn randomly without replacement. Let $X$ be the number of black tokens drawn. We