Concept explainers
a.
To find: the probability of guessing the correct sequence at random.
a.
Answer to Problem 48E
Explanation of Solution
Let E be the event that you guess the correct sequence at random.
Since, there is only 1 possible way that all digits are in correct order. So,
Since, in PIN codes, the digits can be repeated. So, there are 10 ways to choose each of the 4 digits of the sequence. So, total number of possible combinations is:
Thus, the probability of guessing the correct sequence at random is:
b.
To find: the probability of guessing the correct sequence when you recall the first two digits.
b.
Answer to Problem 48E
Explanation of Solution
Let E be the event that you guess the correct sequence when you recall the first two digits.
Since, there is only 1 possible way that all digits are in correct order. So,
Since, in PIN codes, the digits can be repeated. So, there are 10 ways to choose each digits of the sequence. But of the 4 digits, two are already known. So, only two digits need to be guessed. So, the total possible number of combinations is:
Thus, the probability of guessing the correct sequence when you recall the first two digits is:
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning