Skip to main content
Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 4.4.6

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

Guida verificata passo dopo passo
1
Step 1: Understand the structure of a Social Security number. It consists of nine digits, and repetition of digits is allowed. Each digit can range from 0 to 9, giving 10 possible choices for each digit.
Step 2: Recognize that the last four digits are already known from the receipt. Therefore, you only need to randomly select the remaining five digits to match the correct Social Security number.
Step 3: Calculate the total number of possible combinations for the five unknown digits. Since each digit has 10 possible values and repetition is allowed, the total number of combinations is given by \( 10^5 \), which represents 10 choices for each of the 5 digits.
Step 4: Realize that there is only one correct combination of the five unknown digits that matches the Social Security number of the person who was given the receipt.
Step 5: Compute the probability of selecting the correct combination. The probability is the ratio of the number of favorable outcomes (1 correct combination) to the total number of possible outcomes (\( 10^5 \)). This can be expressed as \( P = \frac{1}{10^5} \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting the correct Social Security number from all possible combinations. Understanding how to calculate probability is essential for determining the likelihood of achieving a specific outcome.
Video consigliato:
Percorso guidato
5:37
Introduction to Probability

Combinatorics

Combinatorics is a branch of mathematics dealing with counting, arrangement, and combination of objects. In the case of Social Security numbers, it helps in calculating the total number of possible combinations of digits. Since there are nine digits with repetition allowed, combinatorial principles are crucial for understanding the total outcomes when selecting the digits.

Random Selection

Random selection refers to the process of choosing items from a set in such a way that each item has an equal chance of being chosen. In this scenario, it involves selecting the first five digits of a Social Security number randomly after knowing the last four. This concept is important for understanding how the selection process affects the probability of obtaining the correct number.
Video consigliato:
Percorso guidato
07:09
Intro to Random Variables & Probability Distributions
Pratica correlata
Domanda del libro di testo

Notation When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P (M|B) represent? Is P (M|B) the same as P (B|M)?

155
views
Domanda del libro di testo

Soccer Shootout In the FIFA Women’s World Cup 2019, a tie at the end of two overtime periods leads to a “shootout” with five kicks taken by each team from the penalty mark. Each kick must be taken by a different player. How many ways can 5 players be selected from the 11 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth?

161
views
Domanda del libro di testo

Pick 10 Lottery For the New York Pick 10 lottery, the player first selects 10 numbers from 1 to 80. Then there is an official drawing of 20 numbers from 1 to 80. The prize of \$500,000 is won if the 10 numbers selected by the player are all included in the 20 numbers that are drawn. Find the probability of winning that prize.

209
views
Domanda del libro di testo

Composite Drug Test Based on the data in Table 4-1, assume that the probability of a randomly selected person testing positive for drug use is 0.126. If drug screening samples are collected from 5 random subjects and combined, find the probability that the combined sample will reveal a positive result. Is that probability low enough so that further testing of the individual samples is rarely necessary?

201
views
Domanda del libro di testo

In Exercises 9–12, assume that 100 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.



75 girls.

118
views
Domanda del libro di testo

Radio Station Call Letters Radio and Television station call letters must begin with either K (for stations west of the Mississippi River) or W (for stations east of the Mississippi River) and must include either two or three additional letters. How many different possibilities are there?

152
views