🎲 probability

1. **Stating the problem:** We need to determine which of the given scenarios describe dependent events. 2. **Definition:** Two events are dependent if the outcome or occurrence of

1. **State the problem:** We need to find which probability distribution table has a mean (expected value) of $7$ for the random variable $X$ representing profit. 2. **Recall the f

1. **State the problem:** David makes 7 successful shots out of every 10 free throw attempts. We want to find how many successful shots he will make if he attempts 100 free throws.

1. **State the problem:** We have 60 people surveyed about holiday preferences: Britain, Spain, or Italy. We know:

1. The problem asks which tree diagram correctly represents the sample space of flipping a coin two times. 2. When flipping a coin twice, each flip can result in Heads (H) or Tails

1. The problem involves understanding the sample spaces of compound events when selecting cards labeled J, K, L, M. 2. Each set represents possible ordered pairs of outcomes from t

1. **State the problem:** We want to find the odds against tossing two tails when tossing two coins. 2. **Understand the sample space:** When tossing two coins, each coin can be He

1. **State the problem:** We want to find the probability of getting exactly 2 heads when a coin is tossed 4 times. 2. **Formula used:** The probability of exactly $k$ successes (h

1. **State the problem:** We are given frequencies of students' favorite subjects and need to find the relative frequencies for two combined categories. 2. **Calculate total freque

1. **State the problem:** We want to find how many customers out of 260 are expected to receive either 15% or 25% off their order when spinning a spinner divided into 8 sections wi

1. **State the problem:** We want to estimate the probability of having a thunderstorm on at least 2 of the next 4 days, given each day has a 20% chance of a thunderstorm. 2. **Und

1. **State the problem:** We want to find the probability that a customer bought premium gas given that they paid with a credit card.

1. **Problem statement:** We have two normal six-sided dice, and we want to find the probability that the sum of the two dice is exactly 9.

1. **Problem statement:** A bag contains 5 yellow, 3 green, 6 blue, and 2 black discs. Four discs are chosen at random. Find the probability that: 1) All four discs are the same co

1. **State the problem:** We are given a probability value $p = \frac{5}{100000}$ and need to understand or simplify it. 2. **Express the fraction:** The probability is given as a

1. **State the problem:** We need to find the probability of the union of two events $A$ and $B$ using the formula for not mutually exclusive events. 2. **Formula:** The probabilit

1. The problem involves calculating probabilities of combined events using the addition rule. 2. The addition rule for probabilities states:

1. **State the problem:** We are given probabilities $P(A) = 0.40$, $P(B) = 0.52$, and $P(\text{neither } A \text{ nor } B) = 0.20$. We need to find the probability of the intersec

1. **State the problem:** Given probabilities $P(A) = 0.40$, $P(B) = 0.52$, and $P(\text{neither } A \text{ or } B) = 0.20$, find $P(A \cup B)$. 2. **Recall the formula:** The prob

1. The problem states that the probability of event A occurring is $P(A) = 0.40$. 2. Probability values range from 0 to 1, where 0 means the event never occurs and 1 means the even

1. **State the problem:** We are given two independent events A and B with $P(A) = 3P(B)$ and $P(A \cup B) = 0.68$. We need to find $P(B)$. 2. **Recall the formula for the union of