Solving Combinations
A catering service offers 11 appetizers, 12 main courses, and 10 desserts. A customer is to select 7 appetizers, 8 main courses, and 5 desserts for a banquet. In how many ways can this be done?
Solving Permutations
A panel containing five on-off switches in a row is to be set. Assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
The total number of possible panel settings is (Type a whole number.)
Finding the Probability of Both Independent Events
Two events A and B are independent. The probability of event A happening is 0.3 and the probability of event B happening is 0.5. What is the probability of both events A and B happening?
Finding the Probability for Both Mutually Exclusive Events
A box contains 3 red marbles, 4 white marbles, and 3 blue marbles. If a marble is drawn from the box at random, what is the probability that the marble is either red or blue?
Finding the Conditional Probability for Independent Events
A bag contains 4 red balls and 6 blue balls. If a ball is drawn at random from the bag, what is the conditional probability that the ball drawn is red given that it is not blue?
Determining if Given Events are Mutually Exclusive Events
Suppose a die is rolled and the possible outcomes are {1, 2, 3, 4, 5, 6}. Let Event A be the event that the outcome is an odd number, and Event B be the event that the outcome is less than 4. Are Events A and B mutually exclusive?
Finding the Probability of Both not Mutually Exclusive Events
In a school, 60% of the students play basketball, 45% of the students play baseball, and 30% of the students play both sports. If a student is selected at random, what is the probability that the student plays basketball or baseball?
Finding the Probability of the Complement
A bag contains 5 blue balls, 3 red balls and 2 green balls. If a ball is drawn at random from the bag, what is the probability that the ball drawn is not green?