A six-digit number starts with a number between 3-9 in the first position, with no restrictions on the remaining 5 digits. a) Find the probability that a randomly-chosen phone number contains all different digits. b) Find the probability that a randomly-chosen phone number contains at least one repeated digit. a) Write an expression that models the probability. Select the correct choice below and fill in the answer box(es) within your choice. (Type whole numbers.) A. 1 / (? * 10^5) B. (? * 9P5) / (? * 10^5) C. (? * 10^5) / (? * 9P5) D. 1 / (? * 9P5) The probability that a randomly-chosen number contains all different digits is ?. (Round to four decimal places as needed.) b) The probability that a randomly-chosen number contains at least one repeated digit is ?. (Round to four decimal places as needed.)
Added by Jeremy F.
Close
Step 1
- The first digit can be any number from 3 to 9, giving us 7 options. - Each of the remaining five digits can be any number from 0 to 9, giving us \(10\) options for each. Total possible numbers = \(7 \times 10^5\). Show more…
Show all steps
Your feedback will help us improve your experience
Qudsiya Anis and 67 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In the United States, standard local telephone numbers consist of 7 digits, where the first digit cannot be 1 or 0. A. Find the number of possibilities for telephone numbers. B. Find the probability of randomly selecting a given telephone number from all the possible numbers. C. How many different telephone numbers are possible if only even digits are used? D. Find the probability of choosing a telephone number in which only even numbers are used. E. Find the number of possibilities for phone numbers if the first three digits are 593. What is the probability of randomly choosing a telephone number in which the first three digits are 539?
Varun I.
Assume a 6-digit number is generated at random in the form XXXXXX where each digit, or X, is chosen at random from the range 0-9 inclusive. What are the probabilities of the following situations? 1 - The 6 digit number is an even number or a multiple of 5 2 - The 6 digit number has exactly one 1 and exactly two 2's 3 - The 6 digit number is made up of only 1's and 0's 4 - The 6 digit number is made of 6 consecutive digits (ie: 123456 or 345678 etc..) 5 - There are three sets of the same two digits in the 6 digit number, where the digits can be in any order
Sri K.
You pick 3 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have written the first 3 digits of your phone number? Assume there are no repeats of digits in your phone number. Give your answer as a fraction.
Shaiju T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD