🎲 probability

1. **State the problem:** We want to find the probability that a student pilot passes the written test before the fourth try, given the probability of passing on any single try is

1. The problem asks for the number of elements in the sample space when four students are selected and each is classified as male or female. 2. Each student can be classified in 2

1. The problem asks for the probability of rolling a number less than 3 on a 6-sided die. 2. The possible outcomes on a 6-sided die are $\{1, 2, 3, 4, 5, 6\}$.

1. The problem asks for the probability that the spinner lands on a number less than 8. 2. The spinner has 6 sectors labeled: 9, 4, 5, 6, 7, and 8.

1. The problem asks for the probability of spinning a number less than 8 on a spinner divided into 8 equal sectors labeled 1 through 8. 2. Since the spinner has 8 equal sectors, ea

1. The problem asks for the probability of picking a prime number card from the given set: 3, 4, 5, 6, 7, 8, 9. 2. Identify the prime numbers in the set. Prime numbers are numbers

1. The problem asks to list the elements of sample space $S$ corresponding to event $E$ where at least two of the rivers are safe for fishing. 2. Each letter represents the safety

1. The problem asks to list the elements of sample space $S$ corresponding to event $E$ where at least two of the rivers are safe for fishing. 2. Each element in $S$ is a three-let

1. The problem asks to list the elements of sample space $S$ corresponding to event $E$ where at least two of the three rivers are safe for fishing. 2. Each element in $S$ is a 3-l

1. **State the problem:** We know that 3% of people have questionable objects in their luggage. We want to find the probability that 15 people pass through screening successfully b

1. **State the problem:** We want to find the probability that exactly 2 out of 5 randomly selected speaking characters in movies are females. 2. **Identify the given information:*

1. **State the problem:** We toss a coin 4 times. (a) Illustrate the sample space.

1. The problem asks for the probability that a random variable $x$ is greater than 2 but less than 4, i.e., $2 < x < 4$. 2. To find this probability, we need to know the probabilit

1. **Stating the problem:** We have two shooters, John and Santana.

1. **State the problem:** We have a Markov chain with three states. The transition probabilities depend on the current state. 2. **Given information for transitions from State 3:**

1. The problem asks for the probability that Mrs. Jones will have a baby who is both a boy and has blue eyes. 2. We are given:

1. **State the problem:** We have a box with 2 white and 3 blue marbles, total 5 marbles. 2. We pick two marbles one after the other without replacement.

1. **State the problem:** We are given three pairs of events related to rolling a fair six-sided die. We need to determine if each pair of events is mutually exclusive. If not, pro

1. **State the problem:** We want to estimate the probability of Edward winning the prize wheel after 800 spins, given previous data. 2. **Given data:**

1. The problem states that events X and Y are mutually exclusive, which means they cannot happen at the same time. 2. Given probabilities are $P(X) = \frac{1}{3}$ and $P(Y) = \frac

1. **Problem:** Find the probability of getting an odd number in a single toss of a fair die. Step 1: The sample space for a die toss is $\{1,2,3,4,5,6\}$ with 6 outcomes.