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Many cars have keyless entry. To open the lock, you may
Chapter 12, Problem 980(choose chapter or problem)
Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512.
a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted?
b) How many different ways are there of pressing 5 buttons if repetition is allowed?
c) A burglar is going to press 5 buttons at random, with repetition allowed. What is the probability that the burglar hits the sequence to open the door?
d) Suppose that each button had only one number associated with it as illustrated below. How many different 5-digit codes can be made with the 5 digits if repetition is permitted?
e) Using the buttons labeled 1–5, how many different ways are there to press 5 buttons if repetition is allowed?
f ) A burglar is going to press 5 buttons of those labeled 1–5 at random with repetition allowed. Determine the probability that the burglar hits the sequence to open
the door.
g) Is a burglar more likely, is he or she less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration or as in the second illustration? Explain your answer.
h) Can you see any advantages in labeling the buttons as in the first illustration? Explain.
Questions & Answers
QUESTION:
Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512.
a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted?
b) How many different ways are there of pressing 5 buttons if repetition is allowed?
c) A burglar is going to press 5 buttons at random, with repetition allowed. What is the probability that the burglar hits the sequence to open the door?
d) Suppose that each button had only one number associated with it as illustrated below. How many different 5-digit codes can be made with the 5 digits if repetition is permitted?
e) Using the buttons labeled 1–5, how many different ways are there to press 5 buttons if repetition is allowed?
f ) A burglar is going to press 5 buttons of those labeled 1–5 at random with repetition allowed. Determine the probability that the burglar hits the sequence to open
the door.
g) Is a burglar more likely, is he or she less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration or as in the second illustration? Explain your answer.
h) Can you see any advantages in labeling the buttons as in the first illustration? Explain.
ANSWER:Step 1 of 9
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. We can only forecast the likelihood that an event will occur.