🎲 probability

1. **State the problem:** Priya flips two unbiased coins and rolls a fair five-sided die labeled 1 to 5. The final score $X$ is the number of heads plus the number on the die. We n

1. **Stating the problem:** We are given two events A and B with probabilities:

1. **State the problem:** We are given probabilities for events A and B: $P(A) = 0.6$, $P(A \cap B) = 0.2$, and $P(A \cup B) = 0.9$. We need to find $P(B)$.

1. **Problem statement:** If two events A and B are mutually exclusive and $P(A) = 0.6$ and $P(A \cup B) = 0.8$, find $P(B)$.

1. **State the problem:** There are 16 students in the club, all 7th, 8th, or 9th graders. The probability of choosing a 7th, 8th, or 9th grader is 1, meaning all students are in t

1. **State the problem:** There are 16 students in the swimming club, all from grades 7, 8, or 9. The probability of choosing a 7th, 8th, or 9th grader is 1, meaning all students a

1. **State the problem:** We have a survey of 1,000 university students. - 780 own laptops.

1. **State the problem:** We roll two fair dice and want to find the probability that the sum of the dots on the two dice is less than or equal to 10. 2. **Formula and rules:** The

1. **State the problem:** We need to find the probability that a randomly drawn ball from 25 balls numbered 1 to 25 is either even or a multiple of 8. 2. **Formula for probability:

1. **State the problem:** We want to find the probability $P(E')$ of drawing any card except the 3 of diamonds from a standard 52-card deck. 2. **Formula for probability of the com

1. **State the problem:** We need to find the probability $P(E)$ that a card drawn from a standard 52-card deck is the 3 of diamonds. 2. **Formula for probability:** The probabilit

1. **State the problem:** We need to find the probability $P(E)$ that a card drawn from a standard 52-card deck is a jack. 2. **Recall the formula for probability:**

1. **State the problem:** We are given a Venn diagram with events A and B in a sample space S with equally likely outcomes. We need to find the probability $P(A' \cup B)$, where $A

1. **State the problem:** We are given a Venn diagram with events A and B in a sample space S. We need to find the probability of the union of A and B, denoted as $P(A \cup B)$. 2.

1. **State the problem:** There are 7 people who check their coats, and all claim checks are lost. The coats are returned randomly. We want to find the probability that each person

1. **State the problem:** We have a lock with 4 wheels, each labeled 0 to 9, and the combination is a sequence of 4 digits with no repeats. We want the probability of guessing the

1. **State the problem:** We want to find the probability of having exactly 6 boys and 1 girl in a family of 7 children, where each child is equally likely to be a boy or a girl. 2

1. **State the problem:** We want to find the probability of having 7 girls in a family with 7 children, assuming each child is equally likely to be a girl or a boy. 2. **Formula u

1. **State the problem:** We want to find the probability of having exactly 4 boys and 1 girl in a family of 5 children, assuming each child is equally likely to be a boy or a girl

1. **State the problem:** We need to find the probability of drawing a black queen of diamonds from a standard 52-card deck. 2. **Understand the deck:** A standard deck has 52 card

1. **State the problem:** We need to find the probability that a card drawn from a standard deck of 52 cards is either a black card or a 10. 2. **Recall the formula for probability