🎲 probability

1. **State the problem:** We want to find the probability that Andrew wins the entire tournament. 2. **Identify matches and probabilities:**

1. **State the problem.** The Falcons win each relay race with probability $p=0.8$, and they will race $n=6$ times.

1. **Problem Statement:** The Falcons swim team wins 80% of their relay races and will compete in 6 races this season. We define $W$ as the number of races won.

1. Let's state a basic probability problem: What is the probability of rolling a 4 on a fair six-sided die? 2. The formula for probability is:

1. **Problem Statement:** We have three factories $X$, $Y$, and $Z$ producing components. $D$ is the event that a component is defective.

1. **Problem Statement:** Maya takes a 30-question multiple choice quiz with 5 options each, choosing answers randomly and independently.

1. **Problem Statement:** (a) Given:

1. **Problem Statement:** We want to find the probability that the first card drawn is a spade and the second card drawn is a diamond from a standard 52-card deck.

1. **State the problem:** We want to find the conditional probability that neither die shows a five given that the sum of the two dice is greater than 7. 2. **Define events:**

1. **State the problem:** We have 1000 students surveyed.

1. **Problem statement:** A bug starts at point $B$ and moves randomly along the paths shown in the figure until it reaches one of the traps at points $A$, $F$, or $C$. We want to

1. **State the problem:** Joe answers 10 multiple-choice questions by randomly selecting one of 4 choices (A, B, C, D) with equal probability. We want to find the value of $4^{10}p

1. **State the problem:** We have $6$ jelly beans, $1$ of which is red. We pull out $2$ jelly beans with replacement. We want to find the odds of pulling at least one red jelly bea

1. **State the problem:** We want to find the probability that exactly 2 out of 5 randomly selected laptops are defective, given there are 4 defective laptops out of 24 total. 2. *

1. **State the problem:** We have a box with 10 pens, $x$ of which are red and the rest are blue. Jack randomly picks 2 pens. We want the probability that he picks exactly one red

1. **State the problem:** We have a total of 7 biscuits, with $c$ chocolate biscuits and the rest plain. We want the probability of picking 2 chocolate biscuits when selecting 2 bi

1. **State the problem:** We have a bag with 13 counters: 8 blue and 5 red (since 13 - 8 = 5). 2. **What is asked?** Find the probability that a blue counter is not chosen in two d

1. **State the problem:** We have a pencil case with 8 blue pens and 4 green pens, total $8 + 4 = 12$ pens.

1. **State the problem:** We want to understand for which types of probability distributions the equation $$P(X \leq 5) = P(X < 5) + P(X = 5)$$ holds true. 2. **Recall definitions:

1. **State the problem:** We have $7$ cameras, $4$ defective and $3$ non-defective. We select $2$ cameras with replacement. $X$ is the number of defective cameras in the sample. 2.

1. **State the problem:** We have 14 speedometers total: 12 correctly calibrated and 2 not. We select 3 without replacement. The random variable $x$ is the number of not correctly