A distribution has probabilities 0.10, 0.50, 0.25, and 0.20. Why is it not valid?

A random variable has X = 1, 2, 3 with probabilities 0.2, 0.5, 0.3. What is E(X)?

How many different 4-letter arrangements can be formed from 7 distinct letters without repetition?

Among 30 employees, 18 are full-time and 10 full-time employees have graduate degrees. If an employee is full-time, what is the probability the employee has a graduate degree?

For X = 0, 1, 2 with probabilities 0.25, 0.50, 0.25, what is P(X ≥ 1)?

A survey found 40 students play sports, and 16 of those sports players also play music. If a student is known to play sports, what is P(plays music)?

A bag contains 5 red and 3 blue marbles. Two marbles are selected without replacement. What is the probability both are red?

A standard deck of 52 cards contains 13 hearts. If one card is selected at random, what is the probability it is a heart?

A card is selected from a standard deck. What is the probability of selecting a queen or a king?

Two coins are tossed. Which of the following is the correct sample space?