BackA person's building access code is their first and last initials and four digits.
You know a person's first name only, and you know that the last digit is odd. What is the probability of guessing this person's code on the first try?
Notation What does the symbol ! represent? The five starting players of an NBA basketball team can stand in a line 5! different ways, so what is the actual number of ways that the five players can stand in a line?
In Exercises 5 and 6, use the Fundamental Counting Principle.
6. The state of Virginia's license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible?
Forming License Plates A license plate is designed so that the first two characters are letters and the last four characters are digits (0 through 9). How many different license plates can be formed assuming that letters and numbers can be used more than once?
Forming License Plate Numbers How many different license plate numbers can be made by using one letter followed by five digits selected from the digits 0 through 9?
"Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.
26. Guessing a student's letter grade (A, B, C, D, F) in a class
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"The Birthday Problem
Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:
a. Compute the probability that 10 people have 10 different birthdays. Hint: The first person's birthday can occur 365 ways, the second person's birthday can occur 364 ways, because he or she cannot have the same birthday as the first person, the third person's birthday can occur 363 ways, because he or she cannot have the same birthday as the first or second person, and so on.
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A Flush
A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a flush in five cards.
b. A flush can occur if we get five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive.
"True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false,
explain why.
3. When two events are mutually exclusive, they have no outcomes in common."
Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay \$1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect \$5000.
a. How many different selections are possible?
Jumble Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters MHRHTY were included in newspapers on the day this exercise was written. How many ways can those letters be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.
"Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
36. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ace of spades."