🎲 probability

1. **State the problem:** We have a class of 30 students. 16 have black hair, 11 have brown eyes, and 7 have both black hair and brown eyes. We need to find the values A, B, C in t

1. **State the problem:** We want to find the probability that a randomly chosen person travels to school by car. 2. **Identify the total number of people and the number who travel

1. **Stating the problem:** We are given percentages of students in various faculties and asked to find probabilities related to faculty membership.

1. **State the problem:** A fair coin is tossed four times, and we want to find: a) The sample space.

1. **State the problem:** We have a biased spinner with 5 colors: pink, green, red, yellow, and blue. 2. **Given probabilities:**

1. **State the problem:** We have two fair spinners. The left spinner has numbers 6, 3, 5, and 4. The right spinner has numbers 3, 4, and 4. We spin both and add their results. We

1. **Problem statement:** Complaints about an Internet brokerage firm occur at a rate of 1.1 per day, and the number of complaints follows a Poisson distribution. We want to find t

1. **State the problem:** We need to find the probability that a randomly chosen student earned a grade C. 2. **Recall the formula for probability:**

1. The problem asks to find the probability $P(E)$ where $E$ is the event "an odd number less than 9" from the sample space $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. 2. The formula

1. **State the problem:** We want to find the probability that the first letter in a random arrangement of the letters in "ARIZONA" is A. 2. **Count total letters and repetitions:*

1. **Problem statement:** The letters in the word ARIZONA are arranged randomly. We want to find the probability that the first letter is Z. 2. **Total letters:** The word ARIZONA

1. **Stating the problem:** We have 10 red balls and 5 black balls. Two balls are chosen randomly. We want to find the probability that the two balls chosen are of different colors

1. **Problem Statement:** Find the probability that at least 3 out of 5 randomly selected donors have Group O blood, given $p=0.45$ is the probability an individual has Group O blo

1. **State the problem:** We have two bags with marbles of different colors and quantities. - Bag A: 4 white, 4 purple

1. **State the problem:** We need to find from which bag Greg is less likely to pick a blue tile. 2. **Formula for probability:** Probability of an event = \( \frac{\text{Number of

1. The problem asks for the probability of choosing a white marble from a bag of 25 marbles, where 3 are white. 2. The formula for probability is:

1. **State the problem:** We have a bag with 12 red, 6 blue, 8 green, and 14 brown M&Ms. We draw one M&M 60 times with replacement. We want to predict how many times a red or blue

1. The problem asks us to find the missing probability $p(4)$ in the probability distribution of the random variable $x$. 2. Recall that the sum of all probabilities in a probabili

1. **Stating the problem:** We are given the probability of seeing one penguin in an hour as $\frac{6}{24} = 0.25$ and the probability of seeing more than one penguin in an hour is

1. **State the problem:** We want to find the probability that more than 2 parts are defective out of 7 parts produced by a machine that produces defective parts 12% of the time. 2

1. **Problem statement:** Luisa draws 4 cards without replacement from a standard deck of 52 cards. We want to find the probability that she gets exactly 2 diamonds and 2 hearts in